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Trigonometry Review Guide Sketch each angle and determine the quadrant that contains the angle’s terminal side 1. 2. 110 3. -60 255 Find the measure of each angle from both the positive and negative perspective 4. 5. 20 40 Counterclockwise (Positive) Clockwise (Negative) Counterclockwise (Positive) Clockwise (Negative) Use the correct formulas to convert each measure from degrees to radians or vice versa Degrees 210 Radians 3p 4 -315 108 7p 10 The chart below deals with coterminal angles. If an angle is in degrees, give your answer in degrees. If an angle is in radians, give your answer in radians Angle Reference Angle Positive Coterminal Angle Negative Coterminal Angle 560 -380 9p 4 - 17p 7 1020 43p 5 18632 - 76p 3 361 6. Given an angle measuring 1190 , find a coterminal angle between 0 and 360 7. Given an angle measuring 25p , find a coterminal angle between 0 and 2p 3 Find exact values of sine, cosine, and tan (Hint: Draw triangles) 8. 9. q = 240 q = 315 sin 240 = sin315 = cos240 = cos315 = tan240 = tan315 = NO CALCULATORS Find the exact value of each of the following. Remember to think about where the angle falls on the unit circle and whether you are dealing with x or y. (HINT: Your answers will be -1, 0, or 1) 10. sin180 11. cos180 12. sin p 2 13. cos 90 State whether each expression is positive or negative 14. cos155 15. sin 235 16. sin181 17. cos 45 18. cos- 89 19. tan 210 20. tan 280 21. sin Identify the quadrant being described 22. sin q < 0 cos q < 0 23. cos q > 0 tan q < 0 7p 8 Complete each statement with <, >, or = 24. sin 90 sin 95 25. cos 80 cos 40 26. sin100 sin 80 27. cos115 cos170 28. tan175 tan 40 29. cos- 45 cos- 135 Find the arc length and area of the sector 30. 31. 10 in 5p 3 32. The central angle of a sector is of the sector is 6p in2 ? p 3 r = 6 in 2p q= 5 radians. What is the measure of the radius if the area Answer each question by using the general equation of the sine and cosine function 33. y = 4cos5(x- 2) What is the min and max point? What is the amplitude? How many cycles occur from 0- 2p ? What is the period? What type of shift occurs? Describe the shift. 34. y = 5sin.25(x)- 7 What is the min and max point? What is the amplitude? How many cycles occur from 0- 2p ? What is the period? What type of shift occurs? Describe the shift. Write the equation for the function based on the descriptions provided 35. This sine function’s amplitude is 5. It contains 3 cycles and has been shifted 4 units right. 36. The cosine function’s maximum point is 9 and minimum point is -3. 1 cycle occurs and there was no horizontal shift. 37. The amplitude of this sine function is 8. There are no shifts and the period is 5p . Answer each question about y = sinq or y = cosq 38. In y = sinq , find y if q = 60 39. In y = sinq , find q if y = .707 40. In y = sinq , find three angles in which y = .866 41. In y = cosq , find y if q = 30 42. In y = cosq , if y = .5, find q 43. In y = cosq , find two angles from 0 to 360 in which y = .707