## Sample Midterm 2

1. Express all of the multiples of either
30^{o} or 45^{o} between 0^{o} and
360^{o} in terms of radians.

2. Plot all of the points at the angles in
Problem 1 on the unit circle and find the coordinates of those
points.

3. Graph

for one period starting with x = 0.

4. Verify. (1 - sin x)(sec x + tan x) = cos
x

5. Express the following exactly (using
radicals).

- a) sin105
^{o}
- b) cos105
^{o}
- c) tan105
^{o}

6. Express the following exactly

- a) sin15
^{o}
- b) cos15
^{o}
- c) tan15
^{o}

using the difference formula and the half angle formula.

7. Graph

8. The graph below is the graph of a
function of the form

y = Asin(Bx - C) + D

Find A, B, C, and D.

9. The distance from point A to point B is
measured and found to be 32 meters. What is the horizontal distance
from A to C? How much higher is point B in elevation than point A?

10. The FCC detects an unlicensed radio
transmission from a point C at two detection sites, A and B. It is
known that A and B are 500 meters apart. How far is it from A to C
and how far is it from B to C?

11. A step ladder has two sets of legs. One
set of legs is 8 feet long, and the other set is 7 feet long. When
the ladder is opened the angle between the two sets of legs is 30o.
How far apart are the sets of legs at the bottom of the ladder when
it is opened up? How tall is the ladder when the legs are fully
spread apart?

12. Express the area of the triangle in terms of a, b, and c
without using either angles or trig functions.