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:
a. π/3 radians
b. 19π radians
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.)