Download Trigonometry

Trigonometry
Test #2
Sections 1.5-1.8
Name__________________________________
1. Find the exact value of cos(
 5
).
6
2. Use the triangle below to find sec  .
3
5
θ
3. Use the triangle below to find cot θ.
9
3
θ
.
4. Find the exact value of arccos(-1 / 2).
5. Find the exact value of arctan (1).
6. Evaluate csc( arcos (3/5)).
7. Use an inverse trig function to write θ as a function of x.
3x
θ
3
8. Sketch the graph of f(x) = - sin (x –π) below.
4
2
-5
5
-2
-4
-6
10
9. Sketch the graph of y = sec x + 1 below.
4
2
-5
5
10
-2
-4
-6
10. Your football has landed at the edge of the roof of your school building. When
you are 35 feet from the base of the building, the angle of elevation to your
football is 30 degrees. How high off the ground is your football?
11. How long will it take a plane to climb to an altitude of 10,000 feet, if during its
takeoff its angle of climb is 15 degrees and its speed is 225 feet per second?
(Hint: Find the time it takes to reach 10,000 feet).
Bonus: For the simple harmonic motion described by the trigonometric function
d= 32 cos .5 t, find the least positive value of t for which d = 0.
Take-Home
12. A right triangle has an acute angle θ such that csc θ = ( 7 / 3 ). Find tan θ.
13. 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.
14. Graph y = -4cos (1/2 x) below.
4
2
-5
5
10
5
10
-2
-4
-6
15. Graph
1 

sec x   below.
2 
2
4
2
-5
-2
-4
-6
16. Evaluate sin(arctan
2
).
3
17. Evaluate sin(arcos
4
).
5