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Name: Date: Advanced Math Trigonometric Functions – Review I. Find sin t, cos t, and the tan t when the terminal side of an angle of t radians passes through the given point. 1. (-3, 2) 2. (4, -3) II. Find sin t, cos t, and the tan t when the terminal side of an angle of t radians passes through the given point on the unit circle. 1 3 , 10 10 3. 3 4 , 5 5 4. III. Identify an angle 0 t that is coterminal with the given angle, and find the sine and cosine of the given angle. 9 2 5. 6. 7 4 IV. Identify the quadrant of the terminal side of the angle of t radians. Then determine the sign of sin t, cos t, tan t. 7. 11 8. -23 9. 6.4 10. 17 V. Sketch each angle whose radian measure is given and find its reference angle. 11. 7 3 12. 6 5 13. 3 4 VI. Find the exact value of the sine, cosine, and tangent of each radian value. 14. 7 6 15. 18. 11 6 19. 17 3 10 3 16. 5 4 20. 25 4 17. 3 21. Name: Date: Advanced Math VII. Write each expression as a single real number. 2 22. sin ( ) cos ( ) - cos ( ) sin ( ) 23. cos ( ) cos ( ) + sin ( ) sin ( ) 6 2 6 2 2 3 24. sin ( 3 5 3 5 ) cos ( ) - cos ( ) sin ( ) 4 6 4 6 25. sin ( 7 5 7 5 ) cos ( ) + cos ( ) sin ( ) 3 4 3 4 Answers: 2 1. r 13 sin t 13 cos t 3 13 tan t 2 3 3 4 3 cos t tan t 5 5 4 4 3 4 3 1 cos t tan t 4. sin t sin t cos t tan t 3 5 5 3 10 10 9 9 7 1 7 1 ; cos 0 sin 1 ; cos( ) 6. sin( ) 2 2 2 4 4 4 2 2 QIV : sin t is -, cos t is +, tan t is – Negative x-axis: sin t is 0, cos t is -, tan t is 0 9. QI: all positive 2. r 5 sin t 3. 5. 7. 8. 12. ref. angle = 3 5 7 1 7 3 7 1 ref. angle = 14. sin ; cos ; tan 4 6 2 6 2 6 3 17 3 17 1 17 sin ; cos ; tan 3 3 2 3 2 3 5 1 5 1 5 sin ; cos ; tan 1 4 4 4 2 2 sin 3 0; cos 3 1; tan 3 0 10. QI: all positive 13. 15. 16. 17. 11. ref. angle = 11 1 11 3 11 1 ; cos ; tan 6 2 6 2 6 3 10 3 10 1 10 ) ; cos( ) ; tan( ) 3 19. sin( 3 2 3 2 3 25 1 25 1 25 20. sin( ) ; cos( ) ; tan( ) 1 4 4 4 2 2 18. sin 21. sin( ) 0; cos( ) 1; tan( ) 0 23. 1 2 24. 1 3 2 2 6 2 4 4 3 2 22. 25. 1 3 2 2 6 2 4 4