Instructor: K. W. Nicholson

1. Find the two unknown sides.

2. Use the above triangle for the problems below.

a. If b = 100, C = 120°, and B = 30°, find a.

b. If b = 15, C = 30°, and a = 10, find c.

c. If a = 4, b = 2, and c = 5, find B.

3. Find the trig values without using a calculator:

a. sin 60°

b. cos 225°

c. tan 3p/4

d. sec 300°

e. cot (-240°)

4. Given that p / 2 < u p , and that sin u = 2/3, find the other five trig values of u. Hint : Draw a triangle.

5. A tree 120 yards away and it's top makes an angle of 30° with the horizontal. How tall is the tree? .

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

7. If is in quadrant II, and cot u = -3, find sin u

8. What is the period of ?

9. What is the amplitude of ?

10. Graph 1 cycle of:

a. y = -3 sin x

b. y = 5 cos (x / 2)

c. y = tan (2x)

d. y = 2 sin(3x - 4)

e. y = Sin^-1 x

11. Evaluate:

a. Arc sin (ˆ3 / 2)

b. Arc cos (-1/2)

c. Arc tan 1

d. sin(Arc tan (3/4))

Solve for x on the interval [0,2p]:

Find all solutions on the interval [0,2p)

12. 2cos x sin x - sin x = 0

13. sin² 2x = 1/4

14. sin 2x + cos x = 0

15. cos 4x - 7 cos 2x = 8

16. Given the two points A = (3, 4) and B = (4,-1), find:

a. The vector AB, with tail at A and head at B.
b. The distance from A to B.

17. Given the vector a = (2, -1) and b = ( 1, -3), find:

a. The unit vector in the direction of a.
b. a + b =
c. a - b =
18. Given the two vectors below, draw the vector:

a) V + R
b) R - V

19. a. Express 3 + 4i in polar form.
b. Find all the solutions to z⁴ = 16

20. a. Write the point ( -1, - 3) in polar form.
b. Write (-3, 7p/6 ) in rectangular form.
c. Change r = 3 cos u to rectangular form.
d. Graph r = 2 + sin u