Mathematics 120 (Precalculus)

Review: Examination III

prepared by:

Joseph Malkevitch
Mathematics Department
York College (CUNY)
Jamaica, NY 11451

email: joeyc@cunyvm.cuny.edu
web page: http://www.york.cuny.edu/~malk

1. i. Convert from degrees to radians:

a. 30 degrees
b. 60 degrees
c. 45 degrees
d. -135 degrees
e. 90 degrees
f. -180 degrees
g. -270 degrees
h. 210 degrees
i. 300 degrees
j. 405 degrees

ii. Compute the six trig functions of the angles above.

2. i. Convert from radians to degrees:

c. 13π/6
d. -11π/3
e. 122π
f. 23π/4
g. 51π/2
h. -7π/4
i. -32π

ii. Compute the six trig functions of the angles above.

3. Compute the sin t, cos t and tan t for the situations below:

a. t is quadrant I and sec t = 4

b. t is in quadrant III and cot t = 12/13

c. -t is is in quadrant II and csc -t = 3/2

d. t is in quadrant IV and sec t = 5/(√3)

e. t is in quadrant IV and csc t = -7/(√5)

f. t is in quadrant I and sin t = 4/9

g. t is in quadrant II and cos t = -4/5

4. Draw a graph of y = cos t and y = sin t for 0 ≤ t ≤ 2π.

5. Compute:

a. arc sin 1/2

b. arc tan 1

c. arc cos (√3)/2

6. Graph y = 3 + sin t

7. Graph y = -2 cos t

8. Compute and write the answer in the form a + bi:

a. (2 + i)2 =

b. (3 + 4i)(-1 + 2i) =

c. (3 - 5i)-(7 + 2i) =

d. (-2 + 5i)2 =

e. ((2+5i)/(-1+3i))=

f. ((-2 + 4i)/(3 - 2 i)) =

g. (-3i)3 - (5i)2 + 3i =

9. Graph y = 3x

10. Graph y = -4(2x)

11. Find the value of:

a. 25 - 32(4-2) =

b.

c.

d.

e.

f. 3-2 + (-3)3 =

g

h.

12. Know the trig functions for the 30-60-90 and 45-45-90 triangles.

13. Graph y = 3 log10 x

14. Graph y = - log2 x3

15. Know the formulas for sin 2x and cos 2x. (Yes, memorize them.)