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1. |
If csc  = 2, find sin . |
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A. |
 |
B. |
 |
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C. |
2 |
D. |
 |
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Hint |
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2. |
Complete the identity csc x (cos x - sec x) = ________. |
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A. |
-cot x |
B. |
cot x |
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C. |
tan x |
D. |
-tan x |
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Hint |
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3. |
If sin =  and has its terminal side in the first quadrant, find the exact value of sin 2. |
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A. |
 |
B. |
 |
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C. |
 |
D. |
 |
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Hint |
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4. |
Write the standard form of a line for which the length of the normal segment to the origin is 7 and the normal makes an angle of 120° with the positive x-axis. |
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A. |
x +  y + 14 = 0 |
B. |
x - y + 14 = 0 |
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C. |
x - y - 14 = 0 |
D. |
x + y + 14 = 0 |
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Hint |
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5. |
Write the standard form of the equation of a line for which the length of the normal segment to the origin is 10 and the normal makes an angle of  with the positive x-axis. |
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A. |
x + y - 20 = 0 |
B. |
x - y + 20 = 0 |
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C. |
x + y + 20 = 0 |
D. |
x - y - 20 = 0 |
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Hint |
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6. |
Simplify the expression sin x + 4 cos x + 2 sin -x - 2 cos -x |
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A. |
2 cos x - sin x |
B. |
1 |
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C. |
3 sin x + 2 cos x |
D. |
0 |
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Hint |
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7. |
Find a numerical value of one trigonometric function of x if
sin x (tan x + cot x) = 2. |
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A. |
csc x =  |
B. |
sec x = |
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C. |
cos x = |
D. |
sin x = |
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Hint |
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8. |
Use the sum or difference identity for tangent to find the exact value of tan 165°. |
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A. |
 |
B. |
 - 2 |
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C. |
- |
D. |
1 |
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Hint |
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9. |
Find the value of cos (x - y) if 0 < x <  , 0 < y < , sin x =  , and cos y =  . |
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A. |
 |
B. |
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C. |
 |
D. |
 |
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Hint |
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10. |
Find the value of tan 2 if sin =  and 0 < < . |
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A. |
- |
B. |
 |
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C. |
 |
D. |
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Hint |
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11. |
Solve  + 1 = 2 sin x for all real values of x. |
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A. |
 + 2k |
B. |
+ k |
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C. |
k |
D. |
+ 2k |
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Hint |
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12. |
Solve 4 sin2 x > 3 for 0  x . |
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A. |
 |
B. |
0 x |
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C. |
 |
D. |
 |
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Hint |
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13. |
 PQR has vertices P(5, 8), Q(9, 5), and R(3, 2). Find the length of the altitude of PQR through point P (PQR Is not a right triangle, so there is only one altitude through P). |
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A. |
 |
B. |
 |
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C. |
5 |
D. |
 |
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Hint |
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14. |
PQR has vertices P(5, 8), Q(9, 5), and R(2, 4). Find the equation in standard form of the line that bisects  P. |
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A. |
x - 7y = -67 |
B. |
7x + y = 43 |
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C. |
4x + 3y = -4 |
D. |
3x + 4y = 47 |
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Hint |
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