Download 5.4-5.5 Review

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5.4-5.5 Review
Test Info
 50 points
 Part 1 – 30 points, no calculator
 Part 2 – 20 points, calculator permitted
Prerequisite Material

Finding sin, cos, tan, csc, sec, and cot of angles in both ___________ AND ____________
5.4 Applying Trigonometric Functions

Solving right triangles given _____ and _____________

_______ and solve right triangles for real world applications
5.5 Solving Right Triangles

Solving equations using ___________, __________, and ____________ in degrees AND radians

Evaluating expressions with a mix of trig functions and ____________ trig functions

Solving right triangles given ONLY _________________
APC1: 5.4-5.5 Review
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Practice
I.
Trig values on the Unit Circle
1. sin(225o) = ______
2. cos(30o) = ______
3. tan(300o) = ______
4. csc(240o) = ______
5. sec(180o) = ______
6. cot(270o) = ______
𝜋
7. tan( ) = ______
2
8. cos(
10. sin(
II.
𝜋
2
) = ______
4𝜋
3
) = ______
3𝜋
11. cot( ) = ______
2
9. sec(
5𝜋
4
12. csc(
) = ______
7𝜋
4
) = ______
Solve using inverse trigonometry – write your answers in DEGREES 0 ≤ x < 360o
13. sin(x) =
−√3
2
16. cot(x) = √3
APC1: 5.4-5.5 Review
√2
2
14. tan(x) = −√3
15. cos(x) =
17. sec(x) = –2
18. csc(x) = −√2
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III.
Solve using inverse trigonometry – write your answers in RADIANS 0 ≤ x < 2 𝝅
19. cos(x) =
−√3
2
20. cot(x) = –1
21. sec(x) = 2
22. csc(x) =
2√3
3
23. tan(x) = undefined
24. sin(x) = –1
IV.
Evaluate each expression. Assume that all angles are in Quadrant I.
3
25. sin(arcsin( ))
4
V.
1
26. sec(cos-1( ))
2
27. cot(tan-1(1))
Solving for missing pieces of Triangle ABC
28. If A = 38o and b = 15, find a.
29. If c = 19 and B = 87o, find a.
APC1: 5.4-5.5 Review
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30. If a = 16.5 and B = 65.4o, find c.
31. If a = 38 and b = 25, find A.
32. If c = 19 and b = 17, solve the whole triangle.
33. If A = 43o and c = 102, solve the whole triangle.
APC1: 5.4-5.5 Review
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VI.
Right triangle application problems – draw and solve a triangle to fit the scenario
34. The height of a radio transmission tower is 70 meters, and it casts a shadow of length 30 meters. Find the
angle of elevation of the sun.
35. An observer 2.5 miles from the launch pad of a space shuttle measures the angle of elevation to the base of
the shuttle to be 25o soon after lift-off. How high is the shuttle at that instant?
36. The angle of elevation of the summit of a mountain from the bottom of a ski lift is 33o. A skier rides 1000
feet on this ski lift to get to the summit. Find the vertical distance between the bottom of the ski lift and the
summit.
37. Your cat is trapped on a tree branch 6.5 meters above the ground. Your ladder is only 6.7 meters long. If
you place the ladder’s tip on the branch, what angle will the ladder make with the ground?
APC1: 5.4-5.5 Review
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