Pre Calculus
Name:
Term 1 Final Review
A
1. Find tan 2. Find cos 7
3. Find csc B
C
6
4. Find the measure of angle A.
5. Find the exact value of tan .
6. Find the exact value of cos 540°
7. Find the exact value of sec
8. If sec < 0 and tan > 0, then θ is an angle in quadrant ___.
 3
1
9. Find the angle θ of the ray from the origin to 
, −  in standard position.
2
 2
10. Find the exact value of tan( + ) under the following conditions.
1. cos = −
" , < < ; cos = # ,
< < 2
11. Describe the transformations from the base graph for %(&) = 7 + 5 sin )2 *& + +,
12. Simplify sin(40°) cos(95°) + cos(40°) sin(95°)
13. Prove sin *
14. Prove
+ &+ = − cos &
./0 12
./0 13
15. Simplify
=
456 7
24.4 1
34.4 1
4.4 7
16. Construct and label a reference triangle, then find the six trig functions of the angle θ from the origin to
the point (-8, 15).
17. Use a half angle formula to find the exact value of sin
18. Simplify the expression cos 39° sin 51° + cos 51° sin 39°.
19. In the right triangle ABC, b = 5 and c = 9. Find the measure of angle B.
20. The angle of depression from a point 250 meters from the top of a building is measured to be 13.3o. How
tall is the building?
21. If a wheel with a diameter of 20 inches passes through a central angle of 120o, find the arclength of a
point on the wheel.
22. Find the area of a sector with central angle
and radius 5.
23. Determine the angular velocity in (revolutions per minute) of a car with wheels of radius 15 inches
traveling 75 mph.
24. Graph: = 4 sin * &+ and state the domain, range, amplitude, and period.
25. Graph: = cos *& + + + 3 and state the domain, range, amplitude, and period.
26. Graph : = sec * &+ + 1 and state the domain, range, asymptotes, and period.
27. Graph : = cot *& − + − 2 and state the domain, range, asymptotes, and period.
"
28. Find the exact value of tan(2) under the given conditions: sec = , sin < 0
29. Convert
;
<
into degrees
30. Convert 72° into radians
31. Use a sum/difference rule to find the exact value of sin(255o)
32. Determine csc .
33. Solve for radian value of angle θ.
34. Determine the amplitude of the function %(&) = −2 cos=3(& − )> + 2
35. Determine the period of the function %(&) = −2 cos=3(& − )> + 2
36. Determine the horizontal (phase) shift of the function %(&) = −2 cos=3(& − )> + 2
37. Solve cos =
√
for 0 ≤ θ < 2π .
38. The angle − is coterminal with what angle θ for 0 ≤ < 360° ?
39. Find the exact value of csc when sec = −3 and cot > 0.
40. Find an equation using sine for the following set of data: