Trigonometry Basic Skills Test

You have 30 minutes. You may only use a pen/pencil, and the paper provided. There are ten problems, all of equal weight. You must score 80% or higher. There will be no partial credit, so check your work carefully.

1.

In which quadrant is the terminal side of a an angle whose measure is 1 radian if the initial side of the angle is on the positive x axis and the vertex of the angle is the origin?

2.

Suppose that $\sin(A) = 3/5$ and $\cos(A) = 4/5$, while $\sin(B) = 5/13$ and $\cos(B) = 12/13$. Find $\cos(A+B)$ and $\cos(A-B)$.

3.

Suppose that $\sin(A) = 3/5$ and $\cos(A) = 4/5$, while $\sin(B) = 5/13$ and $\cos(B) = 12/13$. Find $\sin(A+B)$ and $\sin(A-B)$.

4.

Suppose that A is in the first quadrant, and $\tan(A) = 5/6$. Find $\cos(A)$ and $\sin(A)$.

5.

Suppose that the hypoteneuse of right triangle measures 5 meters, and the cosine of one its angles is 3/7. What are the lengths of the other sides of the triangle?

6.

The sine of A is 1/3 and A is in the second quadrant. What is the cosine of A?

7.

Graph $f(x) = \tan(2x)$. Indicate scale and period.

8.

List all $x\in[-2\pi, 2\pi]$ for which $\tan(2x) = 0$.

9.

Using facts about sine and cosine, show that $\tan(A)^2 + 1 = \sec(A)^2$.

10.

What is the radian measure of a central angle in a circle of radius 4 that subtends an arc of 5 units?