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Trigonometry
Test #2
Sections 1.5-1.8
Name__________________________________

1. Find the exact value of cos( ) .
6
2. Use the triangle below to find sec  .
2
7
θ
3. Use the triangle below to find cos θ.
9
5
θ
.
4. Find the exact value of arccos(
3
).
2
5. Find the exact value of arctan ( 3 ).
6. Evaluate tan( arcsin (4/5)).
7. Use an inverse trig function to write θ as a function of x.
θ
x+1
2
8. Sketch the graph of 3 sin (x +π) below.
4
2
-5
5
-2
-4
-6
10
9. Sketch the graph of y = sec x below.
4
2
-5
5
10
-2
-4
-6
10. A man casts a shadow that is 14 feet long. The man is 6 feet tall. What is the
angle of elevation of the sun?
11. What is the speed of a plane (in feet per second) if it takes 3 minutes to climb to
an altitude of 20,000 feet, if during its takeoff its angle of climb is 20 degrees?
12. While traveling across flat land, you notice a hill directly in front of you. The
angle of elevation to the peak is 5°. After you drive 30 miles closer to the
mountain, the angle of elevation is 10°. Approximate the height of the hill.
13. An airplane flying 550 miles per hour has a bearing of S 15° W. After flying for
2 hours, how far south has the plane traveled from its point of departure?
Bonus #1: For the simple harmonic motion described by the trigonometric
function d= .5 sin 20π t, find the least positive value of t for which d = 0.
Take-Home
14. A right triangle has an acute angle θ such that csc θ = ( 7 / 3 ). Find tan θ.
15. A 40-foot extension ladder leans against the side of a building. Find the distance,
h, up the side of the building if the angle of elevation of the ladder is 68 degrees.
16. Graph y = -4cos (1/2 x) below.
4
2
-5
5
10
5
10
-2
-4
-6
17. Graph
1 

sec x   below.
2 
2
4
2
-5
-2
-4
-6
18. Evaluate sin(arctan
2
).
3
19. Evaluate sin(arcos
4
).
5