1. Find an Angle That Is Coterminal to Such That (Answer in Radians)

Trigonometry Test #1 Sections 1.1-1.4

Name______

If the angle given is in radians, then your answer must be in radians. If the angle given is in degrees, then your answer must be in degrees.

13 1. Find an angle  that is coterminal to 5 such that 0    2. (Answer in

radians).

2 2. Find the complement to the angle   . 7

 3. Find the supplement to the angle   . 15

3 4. Convert radians into degrees. 5  5 5. Find the point (x, y) on the unit circle that corresponds to the angle   . 4

6. Find the exact value of cos (-210°).

 5 7. Find the exact value of csc ( ). 3

7 8. Give the exact value of the six trigonometric functions of   . 3 9. Find the value of  given the right triangle below (you may use your calculator and round to two decimal places):

7 10. A right triangle has an acute angle  such that sin  = . Find tan  . 9 1 11. Find the acute angle  , if sin  = . (Radians or degrees) 2

12. Solve for x in the triangle below:

7 30°

13. A man that is 6 feet tall casts a shadow 14 feet long. Find the angle of elevation of the sun. (Angle of elevation is from the ground up). 14. Use the trigonometric identities to verify that cos (1 – sin  )(1 + sin  ) = . Indicate which identities you used. sec

15. Given the point (-3, -5) on the terminal side of angle  . Find  . (You may use your calculator and round your answer to two decimal places). Bonus: In traveling across a flatland, you notice a mountain directly in front of you. The angle of elevation to the peak is 3.5°. After you drive 13 miles closer to the mountain, the angle of elevation is 9°. Approximate the height of the mountain. (Hint: Construct two equations and solve the system by substitution).

3.5° h 9°

13 mi x