Math 113 Test 1 8 Points each Sept. 10, 2001

1. Change to radians:

a. 135°

b. -180°


2. Change to degrees:

a. 3p / 2

d. 5


3. Find the unknown side of the triangle and all six trig values for u .



4. Find the two unknown sides.

5. Find the trig values without using a calculator:

a. sin 60°
b. sin p

c. tan p /4

d. sec 300°


6. If u is in quadrant II, and tan u = -3, find sin u .

7. Find two values of u for 0 ² u ² 2p that satisfy the equation.
cos u = 1/ 2

8. The angle subtended by a ship at a point on the shore is 2°. If the ship is known to have a length of 2000 ft, use the arc length formula to estimate how far the ship is from shore.

9. What is the period of ?

10. What is the amplitude of ?
Sketch the graph, indicating clearly the beginning and ending of the period.

11. y = 4 sin(p x)

12. y = 1 - 2 cos (3x - p )


10 Points Bonus !

An airplane, flying at an altitude of 6 miles, is on a flight path that passes directly over an observer (see figure). If u is the angle of elevation from the observer to the plane, find the distance d from the observer to the plane when u = 30°