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1. |
Complete the identity  _______. |
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A. |
sec x |
B. |
cot x |
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C. |
csc x |
D. |
tan x |
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Hint |
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2. |
Complete the identity
sin  sin (-) - cos  ___. |
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A. |
sin 0 |
B. |
- cos 0 |
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C. |
1 |
D. |
-1 |
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Hint |
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3. |
Use a half-angle identity to find the exact value of sin 67.5°. |
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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. |
Solve sin2 x - sin x + 1 = cos2 x for 0  x < 2 . |
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A. |
0,  ,  , |
B. |
0,  , , |
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C. |
0, ,  , |
D. |
0, , |
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Hint |
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6. |
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. |
 ; 63° |
B. |
; 297° |
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C. |
; 117° |
D. |
; 243° |
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Hint |
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7. |
Find an equation of the line that bisects the acute angles formed by the lines with equations 3x + 4y = 8 and 5x + 12y = 16. |
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A. |
8x + 14y + 23 = 0 |
B. |
14x + 8y - 23 = 0 |
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C. |
8x + 14y - 23 = 0 |
D. |
14x + 8y + 23 = 0 |
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Hint |
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8. |
If sec = 5, find cot . |
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A. |
 |
B. |
 |
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C. |
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D. |
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Hint |
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9. |
Which of the following is a valid trigonometric identity. |
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A. |
Tan2 + cot2 = sec csc |
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B. |
tan + cot = sin cos |
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C. |
tan + cot = sec csc |
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D. |
tan2 + cot2 = sin cos |
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Hint |
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10. |
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. |
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D. |
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Hint |
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11. |
Complete the identity tan ( - A) = ________. |
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A. |
tan A |
B. |
cot A |
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C. |
-tan A |
D. |
-cot A |
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Hint |
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12. |
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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13. |
Write the standard form of the equation of a line for which the length of the normal segment to the origin is 19 and the normal makes an angle of 150° with the positive x-axis. |
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A. |
 x + y - 19 = 0 |
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B. |
x - y + 38 = 0 |
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C. |
x + y - 38 = 0 |
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D. |
x - y + 19 = 0 |
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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. |
x - 7y = -67 |
D. |
7x + y = 43 |
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Hint |
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