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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. |
Express cot (-840°) as a trigonometric function of an angle in Quadrant I. |
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A. |
- tan 60° |
B. |
tan 60° |
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C. |
- cot 60° |
D. |
cot 60° |
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Hint |
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3. |
Find a numerical value of one trigonometric function of x if  |
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A. |
 |
B. |
 |
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C. |
 |
D. |
 |
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Hint |
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4. |
Solve sin x cos x - cos x = 0 for principal values of x. Express solutions in degrees. |
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A. |
150°, 90° |
B. |
30°, 60° |
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C. |
30°, 90° |
D. |
60°, 90° |
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Hint |
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5. |
Consider the equation -x + 2y - 5 = 0. Find the length of the normal and the angle it makes with the positive x-axis. |
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A. |
 ; 297° |
B. |
; 117° |
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C. |
; 63° |
D. |
; 243° |
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Hint |
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6. |
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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7. |
Complete the identity sin4 x - cos4 x = __________. |
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A. |
sin2 x - cos2 x |
B. |
1 |
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C. |
0 |
D. |
tan4 x |
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Hint |
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8. |
If angles x and y are between 0° and 180° such that cos x = - and cos y =  , what is the value of sin (x + y)? |
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A. |
 |
B. |
 |
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C. |
 |
D. |
 |
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Hint |
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9. |
Complete the identity tan ( - A) = ________. |
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A. |
cot A |
B. |
tan A |
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C. |
-cot A |
D. |
-tan A |
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Hint |
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10. |
If cos  =  and has its terminal side in the first quadrant, find the exact value of sin 2. |
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A. |
 |
B. |
2 |
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C. |
 |
D. |
 |
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Hint |
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11. |
Use a half-angle identity to find the exact value of tan  . |
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A. |
- |
B. |
 |
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C. |
- |
D. |
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Hint |
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12. |
Solve sec2 x =  - 2 for -90° < x < 90°. |
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A. |
60° |
B. |
-60°, 60° |
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C. |
-30°, 30° |
D. |
0° |
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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. |
3x + 4y = 47 |
B. |
4x + 3y = -4 |
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C. |
7x + y = 43 |
D. |
x - 7y = -67 |
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Hint |
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