Exercise Set 4.3: Unit Circle Trigonometry
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1 Eercise Set.: Unit Circle Trigonometr Sketch each of the following angles in standard position. (Do not use a protractor; just draw a quick sketch of each angle. Sketch each of the following angles in standard position and then specif the reference angle or reference number.. (a (b (c 7. (a (b (c. (a (b (c. (a. (a (b (b 7 (c (c. (a 9 (b (c. (a 7 (b 8 (c 7. (a 8. (a (b 9 (b (c (c Find three angles, one negative and two positive, that are coterminal with each angle below. 9. (a (b. (a (b 8. (a. (a 8 Answer the following. (b (b 7 9. List four quadrantal angles in degree measure, θ <.. List four quadrantal angles in radian measure, θ <.. List four quadrantal angles in radian measure, < θ.. List four quadrantal angles in degree measure, 8 < θ. 8. (a (b (c 9. (a. (a 7 (b (b. (a 8 (b. (a (c (c 7 7 (c (b 78 (c The eercises below are helpful in creating a comprehensive diagram of the unit circle. Answer the following.. Using the following unit circle, draw and then label the terminal side of all multiples of from to radians. Write all labels in simplest -. Using the following unit circle, draw and then label the terminal side of all multiples of from to radians. Write all labels in simplest Math, Precalculus The Universit of Houston Chapter : Trigonometric Functions
2 Eercise Set.: Unit Circle Trigonometr. Using the following unit circle, draw and then label the terminal side of all multiples of from to radians. Write all labels in simplest 8. Label all the special angles on the unit circle in degrees Using the following unit circle, draw and then label the terminal side of all multiples of from to radians. Write all labels in simplest - 7. Use the information from numbers - to label all the special angles on the unit circle in radians Name the quadrant in which the given conditions are satisfied. 9. ( θ ( θ. ( θ ( θ. ( θ ( θ. ( θ ( θ. ( θ ( θ. ( θ ( θ sin >, cos < sin <, sec > cot >, sec < csc >, cot > tan <, csc < csc <, tan > Fill in each blank with <, >, or =.. sin ( sin (. cos( cos( 7. tan ( tan ( 8. sin ( 9 sin ( 9. cos( cos( 8. tan ( tan ( 9 Math, Precalculus The Universit of Houston Chapter : Trigonometric Functions
3 Eercise Set.: Unit Circle Trigonometr Let P (, denote the point where the terminal side of an angle θ meets the unit circle. Use the given information to evaluate the si trigonometric functions of θ.. P is in Quadrant I and. P is in Quadrant I and. P is in Quadrant IV and. P is in Quadrant III and. P is in Quadrant II and. P is in Quadrant II and Math, Precalculus The Universit of Houston =. =. 8 =. =. =. =. 7 For each quadrantal angle below, give the coordinates of the point where the terminal side of the angle intersects the unit circle. Then give the si trigonometric functions of the angle. If a value is undefined, state Undefined Rewrite each epression in terms of its reference angle, deciding on the appropriate sign (positive or negative. For eample, ( = ( sin sin ( = ( sec sec 7. (a cos( (b tan (. (a sin( (b cot (. (a sin( (b sec. (a csc( 9 (b tan = tan cos =cos cos 7. (a csc 8. (a tan ( (b cot ( (b 9 sec For each angle below, give the coordinates of the point where the terminal side of the angle intersects the unit circle. Then give the si trigonometric functions of the angle An alternate method of finding trigonometric functions of o, o, or o is shown below.. o o o o Diagram Diagram (a Find the missing side measures in each of the diagrams above. (b Use right triangle trigonometric ratios to find the following, using Diagram : ( ( sin ( ( cos ( ( tan sin cos tan (c Repeat part (b, using Diagram. (d Use the unit circle to find the trigonometric ratios listed in part (b. (e Eamine the answers in parts (b through (d. What do ou notice? Chapter : Trigonometric Functions
4 Eercise Set.: Unit Circle Trigonometr. o (a Find the missing side measures in each of the diagrams above. (b Use right triangle trigonometric ratios to find the following, using Diagram : ( ( csc ( ( sec ( ( cot sin cos tan 7 o Diagram Diagram 8 o o Use either the unit circle or the right triangle method from numbers -7 to evaluate the following. (Note: The right triangle method can not be used for quadrantal angles. If a value is undefined, state Undefined. 7. (a tan( (b sin( 7. (a cos( 8 (b csc( 7. (a csc( (b sin( 7 7. (a sec( (b tan ( 7. (a cot ( (b cos( 9 7. (a sin( (b cot ( (c Repeat part (b, using Diagram. (d Use the unit circle to find the trigonometric ratios listed in part (b. (e Eamine the answers in parts (b through (d. What do ou notice? The following two diagrams can be used to quickl evaluate the trigonometric functions of an angle having a reference angle of o, o, or o. Use right trigonometric ratios along with the concept of reference angles, to evaluate the following. (Remember that when converting degrees to radians, =, =, =. o 7. (a sin( (b tan ( 8. (a cos( (b csc( 9. (a cos 7. (a o sin (b (b o sec 7 cot o 77. (a csc( (b 78. (a sin 79. (a sec 8. (a 8. (a csc cot (b (b (b (b 8. (a tan( (b cos cot tan sec 7 sec cos Use a calculator to evaluate the following to the nearest ten-thousandth. Make sure that our calculator is in the appropriate mode (degrees or radians. Note: Be careful when evaluating the reciprocal trigonometric functions. For eample, when evaluating csc( θ on our calculator, use the identit csc( sin ( θ θ = sin ( θ. Do NOT use the calculator ke labeled ; this represents the inverse sine function, which will be discussed in Section.. 8. (a sin ( 7 (b tan ( 8 8. (a tan ( (b cos( 8 8. (a csc( 9 (b cot ( Math, Precalculus The Universit of Houston Chapter : Trigonometric Functions
5 Eercise Set.: Unit Circle Trigonometr 8. (a cot ( (b sec( (a cos 88. (a sin 9 (b csc 7 (b ( cot (a tan (. (b sec( 9. (a csc(.7 (b tan ( 9. Math, Precalculus The Universit of Houston Chapter : Trigonometric Functions
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