# Coterminal And Reference Angles

LESSON 4 COTERMINAL ANGLES Topics in this lesson: 1. Find a positive angle that is coterminal to -30°. On the other end of the spectrum, to find the reference angle for 960 degrees: Determine the quadrant in which the terminal side lies. The reference angle is the acute angle formed by the terminal side of a given angle and the x-axis. You can put this solution on YOUR website! Find a coterminal angle for Q = 15pi/4 terminal side of angle 15pi/4 is 3π/4 so the co-terminal angle is -5π/4 note that both angle together cover 2π radians. The quiz contains questions on finding coterminal angles, reference angles and the values of the six trig functions using right triangles and the unit circle. A reference angle is the smallest angle between the terminal side of an angle and the x-axis. Reference angle. Sometimes, using a negative angle rather than a positive angle is more convenient, or the answer to an application may involve more than one. asked by Kaylen on February 12, 2016; eakin elementary. Relevant page. Solve the problems & select the right answers. Best Answer: Coterminal angles are angles which are the "same", that is, they share the same terminal side. 10270 Apr 15­9:07 AM Sep 10­4:19 PM Nov 11­11:21 AM Reference Angle Cheat sheet: Positive, acute, in all quadrants (how far is it. Byju's Coterminal Angle Calculator is a tool which makes calculations very simple and interesting. 3 3 3 1 O A 3 2π cot = =− =− b. When an angle is not between 0 and 360° ( ), find a coterminal angle that is within that range. In general, when someone is looking for a reference angle, they have a given angle theta to start with. Be sure to show the terminal ray and label the reference angle in your diagram. Coterminal angles are angles formed by different rotations but with the same initial and terminal sides. (a) θ=−2587. Positive Angle. Worksheets are Coterminal angles and reference angles, Coterminal angles, 1, Infinite algebra 2, Draw an angle with the given measure in standard, Angles and angle measure date period, Lesson 4 coterminal angles, 0 1. Improve your math knowledge with free questions in "Coterminal and reference angles" and thousands of other math skills. Start studying Coterminal and Reference Angles. Reference angle: _____. Draw the following angles in standard position, then find the reference angle. Just add OR subtract! Section 6. Coterminal Angle Formula. Reference Angles and Coterminal Angles Mazes. -3750 77t 12. Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. The angle 11 4 πis. The word "coterminal" is slightly confusing, but all it's meant to denote is angles that terminate at the same point. What is the terminal side?. Find a coterminal angle between 0° and 360°. THE DEFINITION AND EXAMPLES OF REFERENCE ANGLES Definition The reference angle of the angle T, denoted by T'. Best Answer: 445 what? Degrees? The "next" to me implies that it is greater than 445 degrees but, because of "smallest," you want the one that isn't greater than one revolution greater than 445 degrees. -1-Find the measure of each angle. You can sketch the angles and often tell just form looking at them if they are coterminal. Reference angles must be. Using the unit circle below, explain how you can find the sine of any given angle, both by the ratio (opposite over hypotenuse) and by the ordered pairs. D: 450 and -270 with 450, we subtract 360 to get 90, which will satisfy the coterminal angles. All of these angles are coterminal angles. a) 4 11 b) 395° c) 3 2 d) -45° 15. ­777 Reference Angles ­ an acute angle (< 90), that is formed by the terminal side & x­axis. The reference angle $$\text{ must be } 90^{\circ}$$ In radian measure, the reference angle $$\text{ must be } \frac{\pi}{2}$$ Basically, any angle on the x-y plane has a reference angle, which is always between 0 and 90 degrees. 1: Coterminal & Reference Angles Pre­Calculus August 20, 2015 Usefulness of coterminal angles: Find an angle between 0 and 360 that is coterminal with each angle. When an angle is not between 0 and 360° ( ), find a coterminal angle that is within that range. An angle's reference angle is the measure of the smallest, positive, acute angle t formed by the terminal side of the angle t. This article explains what a reference angle is, providing a reference angle definition. +/- angles, coterminal angles and values of trig functions What are some tips or tricks you would give to someone who is just starting to learn about positive and negative angles, coterminal and reference angles, and the values of trig functions?. (a) -135o (b) 1200o Reference Angles REFERENCE ANGLE: a positive acute angle made by the terminal side of an angle and the x-axis. Answers can vary. For any angle α, the positive coterminal angle can be found by: α + 360°∙n , if α is given in degrees, where n=0,1,2,3,. It must be less than 90 degree, and always positive. 510 degrees 3. I N THE RADIAN SYSTEM of angular measurement, the measure of one revolution is 2 π. Examples: • 60° and 30° are complementary angles. (For negative angles add 360 instead). 10270 Apr 15­9:07 AM Sep 10­4:19 PM Nov 11­11:21 AM Reference Angle Cheat sheet: Positive, acute, in all quadrants (how far is it. 2 radians (see Figure 6a) and the reference angle for −137 is 180 ( ) + −137 =43 (see Figure 6b). To find the coterminal angle of -690° we could add 360 because it is negative (subtract if positive) so: -690+360 =-330 and -330+360=30° So the smallest positve coterminal angle of -690° is 30°. asked by tj on October 6, 2010; Pre-Calc. Relevant page. e To find a NEGATIVE coterminal (if in deg) (if in rads) (I call these "swirlies") e Coterminal angles can contain Example 2a: Find a positive and negative coterminal angle for the given angle 0. (In the next Topic, Arc Length, we will see the actual definition of radian measure. #trigonometry #anglesintrigonometry Category. Quadrant Angle Measure (radians) Angle Measure (degrees) Coordinate on Terminal Side of Angle 1 2 3 4. 2 Angles and Radian Measure 471 Finding Coterminal Angles In Example 1(b), the angles 500° and 140° are coterminal because their terminal sides coincide. For example: Find the standard coterminal angle for a. moomoomath. Reference Angle Worksheet Give the reference angle for each angle below. The reference angle is the positive acute angle that can represent an angle of any measure. kcl e Unit Circle: Right Triangle Trigonometry D4 Notes Reference Angles & Exact Values Reference Angles: Special Right Triangles: 300 Name: Coterminal Angles: ABIes CO-MC. W C eAtlhlS lrxipgZhztRsN orAeYsreMrsvwegdz. The first example we did was: Find θ, given that tan θ = 0. h T JMKaHdMeD jwTistyh0 cI7n7fliKnQidtGeu cAzlggPerbar qab 62p. Fab Five for Trigonometry Level Three: Reference Angles, Coterminal Angles, Linear Speed and Angular Speed - Kindle edition by Kathryn Gniadek. It is reflects Algebra 2 (algebra ii) level exercises. The reference angle is the smallest angle between the terminal side of the angle and the x-axis. asked by Kaylen on February 12, 2016; eakin elementary. 13) −330 ° 30 ° 14) −435 ° 285 ° 15) 640 ° 280 ° 16) −442 ° 278 ° Find a coterminal angle between 0 and 2222ππππ for each given angle. Mathematics. Reference Angles and Triangles - Independent Practice Worksheet Complete all the problems. Trig Worksheet-Day 2 (Coterminal Angles & Angle Conversions) Determine two coterminal angles (one positive and one negative) for each angle. Coterminal angles: are angles in standard position (angles with the initial side on the positive x-axis) that have a common terminal side. 13-2 Angles of Rotation 937 Coterminal angles are angles in standard position with £ÓäÂ Ó{äÂ Þ Ý the same terminal side. Best Answer: Coterminal angle in radians = (angle in radians) +- (k)(2π) Since k can be any integer, therefore there can be an infinite number of coterminal angles for any angle. NOTE: Only your test content will print. There are an infinite number of coterminal angles that can be found. Converting between degrees and radians. Following this procedure, all coterminal angles can be found. Find a coterminal angle between 0° and 360°. Upon this discovery, I asked them how they could tell if two angles were coterminal based on this. Solving Triangles a. To find the coterminal angle of an angle, simply add or subtract radians, or 360. The reference angle is always positive. Solve advanced problems in Physics, Mathematics and Engineering. Start below. EXERCISES: 1. We can list all angles coterminal to the angle x using the shorthand notation x + 2n, n an integer. Therefore, the reference angle is always coterminal with the original angle θ. If an input is given then it can easily show the result for the given number. 1 COTERMINAL AND REFERENCE ANGLES. By simply. 21) −330 ° 30 ° 22) −435 ° 285 ° 23) 640 ° 280 ° 24) −442 ° 278 ° Find a coterminal angle between 0 and 2222 πππ for each given angle. Coterminal angles. Given the angle Quadrant Coterminal Angle(-) find the following: Il. asked by tj on October 6, 2010; Pre-Calc. Give your answers in radians. For example, 100° and 460° are coterminal for this reason, as is −260°. If you examine the equation above, you will see that we are just adding or subtracting 2π radians (=360º) to the angle to find it's coterminal. 13) −330 ° 30 ° 14) −435 ° 285 ° 15) 640 ° 280 ° 16) −442 ° 278 ° Find a coterminal angle between 0 and 2222ππππ for each given angle. Two Angles are Complementary when they add up to 90 degrees (a Right Angle). (look below). So I now give the student the angle 3pi/5 to find a reference angle. Give 2 coterminal angles, one positive and one negative for each of the following. 342 62/87,21 All angles measuring are coterminal with a 342 DQJOH Sample answer: Let n = 1 and í1. 8along with the Quotient and Reciprocal Identities in Theorem10. Reference and Coterminal Angles Find a positive and a negative coterminal angle for each given angle. This trigonometry video tutorial explains how to find a positive and a negative coterminal angle given another angle in degrees or in radians using the unit circle. Are reference angles and radians the same? No. They can be positive or negative integers. Start below. Fab Five for Trigonometry Level Three: Reference Angles, Coterminal Angles, Linear Speed and Angular Speed - Kindle edition by Kathryn Gniadek. 4 in your book. THE REFERENCE ANGLE THEOREM Reference Angle Theorem: If θis an angle, in standard position,that lies in a quadrant and αis. Worksheet – Coterminal, Reference, and Special Angles Find two angles (one in a clockwise direction and the other in a counterclockwise direction, from the given angle) that are coterminal to the following:. (a) -135o (b) 1200o Reference Angles REFERENCE ANGLE: a positive acute angle made by the terminal side of an angle and the x-axis. 212° - ° 6. There are an infinite number of coterminal angles that can be found. Coterminal Angles are two angles in standard position with the same terminal side. THE DEFINITION AND EXAMPLES OF COTERMINAL ANGLES Definition Two angles are said to be coterminal if their terminal sides are the same. 10270 Apr 15­9:07 AM Sep 10­4:19 PM Nov 11­11:21 AM Reference Angle Cheat sheet: Positive, acute, in all quadrants (how far is it. Coterminal and reference angles calculator keyword after analyzing the system lists the list of keywords related and the list of websites with related content, in addition you can see which keywords most interested customers on the this website. When a circular cake is cut up into four equal pieces, each piece has a right angle at the center. 3 General Angles. If the measure of the original angle is given in degrees, its reference angle must also be in degrees. Learn the basics of trigonometry: What are sine, cosine, and tangent? How can we use them to solve for unknown sides and angles in right triangles?. 3 Coterminal Angles and Evaluating Trig Function for Angles Lesson 8. 12 12 117t 15 os IS Sketch a picture and determine the Reference Angle for each find coterminal angles if needed). _ Coterminal Angles 2. 25) 11 π 3 5π 3 26) − 35 π 18 π 18 27) 15 π 4 7π 4 28) − 19 π 12 5π 12 Find a positive and a negative coterminal angle for each given. Find the reference angle for the following. Let n represent any integer. Find one positive angle and one negative angle that are coterminal with each angle. Coterminal Angles are two angles in standard position with the same terminal side. If the angle is in the first quadrant, then the reference angle is the original angle. In degrees: You can add or subtract $360˚$ however many times you want, and the new angle will always be coterminal to the original angle. (More about the reference angle in Objective 5. Any angle θ is coterminal with θ + 360° -- because we are just going around the circle. Coterminal angle calculator that returns exact values and steps given either a degree or radian value, Trigonometry Calculator Identity Reference. Angles in quadrant I. 2 Angles and Radian Measure 471 Finding Coterminal Angles In Example 1(b), the angles 500° and 140° are coterminal because their terminal sides coincide. Determine the cosine of 23pi/4, 13pi/3, and 37pi/6 using reference angles. There are an infinite number of coterminal angles that can be found. Standard Coterminal Angles If you are asked to find a standard coterminal angle, that means the answer needs to be between 00 and 3600. Best Answer: Coterminal angle in radians = (angle in radians) +- (k)(2π) Since k can be any integer, therefore there can be an infinite number of coterminal angles for any angle. Reference Angle Ordered Pair Degrees O Coterminal Angle(-) find the following: I. 3 04 Reference Angle: Coterminal Angle: Determine the reference angle and at least one coterminal angle for each angle drawn below. Trig Quiz Chapter 5 Sections 1-3. Best Answer: 445 what? Degrees? The "next" to me implies that it is greater than 445 degrees but, because of "smallest," you want the one that isn't greater than one revolution greater than 445 degrees. Leave your answer in the form that was given (radians or degrees). It is reflects Algebra 2 (algebra ii) level exercises. Notes ­ Coterminal Angles April 27, 2015 Coterminal Angles Lesson objectives Teachers' notes Identify the quadrant of a terminal side. o o o A positive angle is A negative angle is. Coterminal angles are angles which share the same initial side and terminal sides. It is reflects Algebra 2 (algebra ii) level exercises. The reference angle is †§ = 180° º 150° = 30°. -1500 a:5!:l_ ~ Find two angles (one inaclockwise direction and the other inacounterclockwise. This article explains what a reference angle is, providing a reference angle definition. These two angles are coterminal; see Fig. Answers need to be in the same measure as the given angle. Exercises on Angles of Rotation - Coterminal Angles. Algebra -> Trigonometry-basics-> SOLUTION: what is the coterminal angles of the following: 1. Trigonometric ratios of angles in radians. Coterminal angles are two angles that are drawn in the standard position (so their initial sides are on the positive x-axis) and have the same terminal side like 110° and -250° Another way to describe coterminal angles is that they are two angles in the standard position and one angle is a multiple of 360 degrees larger or smaller than the other. Refer Reference Angles; 7-5; Reference Angles; Reference Angles; me and sarah are currently in the apple store, and Reference Angles; Unit circles and reference angles. Coterminal Angles Find two coterminal angles for each given angle. Coterminal angles: are angles in standard position (angles with the initial side on the positive x-axis) that have a common terminal side. This is the acute angle formed by the terminal side of the given angle and the X-axis. Reference Angles (Guided) PC-Trigonometry- Rotations and the Unit Circle- Finding Reference Angles. Since there are an infinite number of coterminal angles, this calculator finds the one whose size is between 0 and 360 degrees or between 0 and 2π depending on the unit of the given angle. For each angle in standard position, find two positive angles and two negative angles that are coterminal with the given angle. The tangent function is negative in Quadrant II, so you can write: tan (º210°) = ºtan 30° = º b. A calculator to find the exact value of a coterminal angle to a given trigonometric angle. For example 30 ° , − 330 ° and 390 ° are all coterminal. Reference Angle. Coterminal definition, having a common boundary; bordering; contiguous. How to Compute the Measure of the Reference Angle of an Angle in Standard Position Terminal Side In Quadrant I Quadrant II Quadrant III Quadrant IV Reference Angle (θin degrees) θ Reference Angle (θin radians) θ 180q T S T T 180q 360q T T S 2S T. I begin working with special angles because students will need to use these angles the most through the rest of the year. - 310° Find the complement and supplement for the given angles. Angles, Angular Conversions, and Trigonometric Functions. How do you write an expression to represent every angle coterminal to s? Given: s in a unit circle with point (-1/2 , -sqrt(3)/2) I got that it is quadrant 3, and the trig functions are those of angle 60°. QUESTION: Find the reference angle for. Reference angle is the smallest positive acute angle formed by the x-axis and the terminal side. I don't want students to think that the numerator is always just pi on a reference angle. Finding the reference angle. About This Quiz & Worksheet. Coterminal Angles are angles that start and stop in the same place. Answers can vary. THE REFERENCE ANGLE THEOREM Reference Angle Theorem: If θis an angle, in standard position,that lies in a quadrant and αis. SOLUTION a. Coterminal angles are angles formed by different rotations but with the same initial and terminal sides. REFERENCE ANGLES ARE ALWAYS POSITIVE! To find a reference angle for angles outside the interval 0o < θ < 360o or 0π < θ < 2π you must first find a corresponding coterminal angle in this interval. Reinforce the concept of reference and coterminal angles with the multiple response worksheets featured here. Then find and draw one positive and one negative angle coterminal with the given angle. a) b) c) d)38 27 72 58 a) b) c) d) a) b) c) d) a) b) c) d) What!are!the!possible!positive!and!negative!coterminal!angles!of!320 ? 680 ,!±40 1040 ,!±400 675 ,!±45. All angles throughout this unit will be drawn in standard position. Best Answer: 445 what? Degrees? The "next" to me implies that it is greater than 445 degrees but, because of "smallest," you want the one that isn't greater than one revolution greater than 445 degrees. 1) −5° 2) 5° 3) 45 ° 4) −45 ° 5) 5 π 2 6) −π 7) 17 π 9 8) 13 π 18 State if the two given angles are coterminal or not. Find all coterminal angles for each angle such that -360° < θ < 360°. 5 1radians is 7. cs/coterminal-angles. There are an infinite number of ways to draw an angle on the coordinate axes. Determine if you are moving clockwise or. Note how the reference angle always remain less than or equal to 90°, even for large angles. 6 Coterminal Angles Notes. Tt from positive coterminal angle 44 of 45 16. Reference Angles and Coterminal Angles MazesStudents will practice identifying reference angles and coterminal angles given angles in degrees and radians. The key to solving a reference angle is to understand which quadrant the angle lies in. There are two methods that can. One way to find the measure of an angle that is coterminal with an. Find the reference angle for the following. coterminal angles is as simple as adding or subtracting 360 ° or 2π to each angle, depending on whether the given angle is in degrees or radians. -1- ©z 62f0q1i2J XKuugt6aa ASTo1fntVwuaKrDeB WLfLxCm. In this calculus worksheet, learners identify terminal and coterminal angles using the unit circle. 1) 326 ° 686 ° and −34 ° 2) 530 ° 170 ° and −190 ° 3) −215 ° 145 ° and −575 ° 4) −84 ° 276 ° and −444 ° 5) 215 ° 575 ° and −145 ° 6) 255 ° 615 ° and −105 ° 7) −660 ° 60 ° and −300 ° 8) −255 °. Identify all angles that are coterminal with each angle. Be sure to show the terminal ray and label the reference angle in your diagram. Sketch both angles on the unit circle provided. If you examine the equation above, you will see that we are just adding or subtracting 2π radians (=360º) to the angle to find it's coterminal. 45o All angles have a measure of 45 + 360k, where k is an integer, are coterminal with 45. We are experts in trigonometry. Math Expression Renderer, Plots, Unit Converter, Equation Solver, Complex Numbers, Calculation History. between 0 and 360°. Quadrant I Quadrant II Quadrant III Quadrant IV reference reference 180 reference 180 reference 360 State the quadrant of each given. 2_practice_solutions. 62/87,21 All angles measuring are coterminal with a UDGLDQDQJOH Sample answer: Let n = 1 and í1. and the closest x­axis is its reference angle. Find the reference angle. The previous examples suggest a pattern in finding reference angles based on their quadrant. Angles in Standard Position: C-øu. An angle's reference angle is the size of the smallest acute angle,$\,{t}^{\prime },$formed by the terminal side of the angle$\,t\,$and the horizontal axis. Just add OR subtract! Section 6. Best Answer: 2pi/3 a full cycle is 2pi (360 degrees), so to find a coterminal angle, add 2pi or subtract 2pi to the angles you are given, so Add 2pi to find a positive angle coterminal to it 2pi/3 + 2pi = 8pi/3 Then you could add another 2pi to find another coterminal angle, so 8pi/3 + 2pi = 14pi/3. Sometimes, using a negative angle rather than a positive angle is more convenient, or the answer to an application may involve more than one. You can see that a negative angle can be coterminal with a positive one. 7) -470° x. Coterminal Angles are angles who share the same initial side and terminal sides. 21) −330 ° 30 ° 22) −435 ° 285 ° 23) 640 ° 280 ° 24) −442 ° 278 ° Find a coterminal angle between 0 and 2222 πππ for each given angle. USING A REFERENCE ANGLE TO FIND THE VALUE OF THE SIX TRIGONOMETRIC FUNCTIONS 1. Trigonometry Finding Angles, Coterminal Angles, Reference Angles (TFACARA) Find the measure of each angle. Finding Coterminal Angles algebraically is a little more challenging: First, we have to decipher what the question is asking. Using the picture shown below of a non-special angle on the Unit Circle. There are an infinite number of ways to draw an angle on the coordinate axes. Coterminal Angles Two angles that are in standard position and share a common terminal side are said to be coter-minal angles. Mathematics. asked by tj on October 6, 2010; Pre-Calc. Find a coterminal angle between 0° and 360°. Draw each angle, θ, in standard position. 6 5π − is coterminal with 6 7π which terminates in Quadrant III. Fun maths practice! Improve your skills with free problems in 'Coterminal and reference angles' and thousands of other practice lessons. Students use their solutions to navigate through the maze. For any angle α, the positive coterminal angle can be found by: α + 360°∙n , if α is given in degrees, where n=0,1,2,3,. And, most important, each right angle is half. This will help your child to distinguish between the various types of angles. Best Answer: 445 what? Degrees? The "next" to me implies that it is greater than 445 degrees but, because of "smallest," you want the one that isn't greater than one revolution greater than 445 degrees. A useful tool for finding values of trigonometric functions of certain angles (you’ll learn how to do that later) is the reference angle. Consider the following two angles: 210° and -150°. 4 Coterminal and Reference Angles Objectives: 1. Take your time, as you have all the time in the world. Otherwise, for each angle do the following: If the angle is positive, keep subtracting 360 from it until the result is between 0 and +360. To find the coterminal angles, simply add or subtract 360 degrees as many times as needed from the reference angle. Download it once and read it on your Kindle device, PC, phones or tablets. Trigonometric Angles formulas list online. This smart calculator is provided by wolfram alpha. Answers can vary. For each angle in standard position, find two positive angles and two negative angles that are coterminal with the given angle. Reference and Coterminal Angles Find a positive and a negative coterminal angle for each given angle. Finding coterminal angles is as simple as adding or subtracting 360° or 2π to each angle, depending on whether the given angle is in degrees or radians. Remove Ads. find the least positive degree of an angle that is coterminal with an angle of the following measurment. What is the terminal side?. Scholars explore the relationships between the angle and reference angles along with coterminal angles. A negative angle is 45° 360°( 2) or 675°. The coterminal angles can be positive or negative. Learn More. Trigonometry: Reference Angles Science and Mathematics Education Research Group Supported by UBC Teaching and Learning Enhancement Fund 2012-2013 Department of Curriculum and Pedagogy a place of mind F A C U L T Y O F E D U C A T I O N. Every angle, θ (the Greek letter theta), has a reference angle, , associated with it. (look below). Coterminal angles are found by adding/subtracting 360 degrees (for degree angle measure) or 2pi (for radian angle measure) to/from the given angle. To determine coterminal angles for a given angle. Coterminal definition, having a common boundary; bordering; contiguous. An angle's reference angle is the measure of the smallest, positive, acute angle t formed by the terminal side of the angle t. Ex 2: Find one positive and one negative angle that are coterminal to 112º. If θ is an acute angle is standard position and B (-3, 4) is a point on the terminal side of the angle, what is the value of. Following this procedure, all coterminal angles can be found. FINDING COTERMINAL ANGLES 3. Coterminal angles: are angles in standard position (angles with the initial side on the positive x-axis) that have a common terminal side. For example: Find the standard coterminal angle for a. Intro to Video: Reference Triangles and Sine, Cosine, and Tangent; Overview of Reference Triangles, Reference Angles, and SOH-CAH-TOA; Theorem for Reference Triangles and Trigonometric Functions with Examples. Use the below online coterminal angle calculator to find out the positive and negative coterminal angles for the given angle by entering angle value in the input field. Using our calculators, we found that θ = tan-1 0. 68% average accuracy. So suppose the given angle has this property, i. Draw the angle in standard position b. For example 30°, -330° and 390° are all coterminal. -3750 77t 12. Coterminal Angles are angles who share the same initial side and terminal sides. Coterminal Angles. All of the angles in the following figure are coterminal with an angle of degree measure of 45°. It also shows you how to. Draw each angle, θ, in standard position. Reference Angles and Coterminal Angles Draw an angle with the given measure in standard position. To preview this test, click on the File menu and select Print Preview. -xative coterminal angle. I understand perfectly how to find the reference angle for a degree, such as 150 degress = reference angle of 30 degrees, because the 2nd quadrant goes from 90 to 180 degrees, so you simply subtract 150 from 180 to come up with 30. Function Values. Four Examples – Find a coterminal angle within a specified domain; Reference Triangles. Identify all angles coterminal with the given angle. Reference angles are typically used in trigonometric theorem problems. The first example we did was: Find θ, given that tan θ = 0. Scroll down the page for more examples and solutions. Draw the angle in standard position Reference angle. Name four angles between 00 and 3600 with a reference angle of 200 If each angle is in standard position, determine a coterminal angle that is between 00 and 3600. But if an angle is less than 90 degrees, so, for example, both of these angles that we started our discussion with are less than 90 degrees, we call them "acute angles. the clockwise direction, this angle has a measure of –270°. What I've done so far. So that is an acute angle, and that is an acute angle right over here. My question. Find positive and negative coterminal angles. Find the reference angle, α. Jan 29­9:53 AM. If angle is measured in degrees, add or subtract 360 If angle is measured in radians, add or subtract 2 Examples: Find a positive and a negative angle coterminal with the given angle. a) 460° b) 350° 0. A reference angle is the smallest angle between the terminal side of an angle and the x-axis. Trig Worksheet-Day 2 (Coterminal Angles & Angle Conversions) Determine two coterminal angles (one positive and one negative) for each angle. 1400/ Convert to radians. For each of the following angles,. In figure let the initial side is OX. The formulas above would only yield one of each co terminal angles. There are four unique mazes included. 1) -100° y 2) 1020° y x x 60° 80° 3) -130° y 4) 160° y 70° x x 50° 5) -290° y 6) -780° y 20° x x 60° Draw an angle with the given measure in standard position. Let n represent any integer. Learn the basics of trigonometry: What are sine, cosine, and tangent? How can we use them to solve for unknown sides and angles in right triangles?. Coterminal Angles. REFERENCE ANGLES ARE ALWAYS POSITIVE! To find a reference angle for angles outside the interval 0o < θ < 360o or 0π < θ < 2π you must first find a corresponding coterminal angle in this interval. Unit Circle Trigonometry Labeling Special Angles on the Unit Circle Labeling Special Angles on the Unit Circle We are going to deal primarily with special angles around the unit circle, namely the multiples of 30o, 45o, 60o, and 90o. Download it once and read it on your Kindle device, PC, phones or tablets.