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1. Rewrite the following expression as an equivalent expression that doesn't contain powers of trigonometric functions greater than 1.
8cos2x
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A. 1 + cos 2x
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B. 4 + 4 cos 2x
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C. 16 cos x
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D. 4 – 4 cos 2x
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2. Find all solutions to the following equation:
sinx csc x = –2 sin x
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A.
/var/folders/9s/5k_n9ntx3sg2tkk2k98jfw200000gn/T/com.microsoft.Word/WebArchiveCopyPasteTempFiles/350664RR_Q43_7pi-plus-npi.png
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B.
/var/folders/9s/5k_n9ntx3sg2tkk2k98jfw200000gn/T/com.microsoft.Word/WebArchiveCopyPasteTempFiles/350664RR_Q43_pi-plus-npi.png
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C.
/var/folders/9s/5k_n9ntx3sg2tkk2k98jfw200000gn/T/com.microsoft.Word/WebArchiveCopyPasteTempFiles/350664RR_Q43_7pi-plus-2npi.png
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D.
/var/folders/9s/5k_n9ntx3sg2tkk2k98jfw200000gn/T/com.microsoft.Word/WebArchiveCopyPasteTempFiles/350664RR_Q43_pi-plus-2npi.png
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3. Use the given information to find the exact value of the expression.
tan α = 21⁄20, α lies in quadrant III, cos β = –5⁄13, and β lies in quadrant II.
Find sin(α + β).
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A.
/var/folders/9s/5k_n9ntx3sg2tkk2k98jfw200000gn/T/com.microsoft.Word/WebArchiveCopyPasteTempFiles/350664RR_Q14_352-over-377.png
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B.
/var/folders/9s/5k_n9ntx3sg2tkk2k98jfw200000gn/T/com.microsoft.Word/WebArchiveCopyPasteTempFiles/350664RR_Q14_345-over-377.png
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C.
/var/folders/9s/5k_n9ntx3sg2tkk2k98jfw200000gn/T/com.microsoft.Word/WebArchiveCopyPasteTempFiles/350664RR_Q14_minus-152-over-377.png
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D.
/var/folders/9s/5k_n9ntx3sg2tkk2k98jfw200000gn/T/com.microsoft.Word/WebArchiveCopyPasteTempFiles/350664RR_Q14_minus-135-over-377.png
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4. Find the exact value by using the sum or difference identity:
cos (135° + 120°)
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A.
/var/folders/9s/5k_n9ntx3sg2tkk2k98jfw200000gn/T/com.microsoft.Word/WebArchiveCopyPasteTempFiles/350664RR_Q11_minus-sqrt2-sqrt3-plus-1.png
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B.
/var/folders/9s/5k_n9ntx3sg2tkk2k98jfw200000gn/T/com.microsoft.Word/WebArchiveCopyPasteTempFiles/350664RR_Q11_sqrt2-sqrt3-plus-1.png
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C.
/var/folders/9s/5k_n9ntx3sg2tkk2k98jfw200000gn/T/com.microsoft.Word/WebArchiveCopyPasteTempFiles/350664RR_Q11_minus-sqrt2-sqrt3-minus-1.png
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D.
/var/folders/9s/5k_n9ntx3sg2tkk2k98jfw200000gn/T/com.microsoft.Word/WebArchiveCopyPasteTempFiles/350664RR_Q11_sqrt2-sqrt3-minus-1.png
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5. Express the following sum or difference as a product:
cos 2x – cos 4x
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A. -2 sin 3x sin x
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B. cos (–2x)
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C. 2 sin 3x sin x
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D. –2 cos 3x sin x
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6. Complete the following identity: /var/folders/9s/5k_n9ntx3sg2tkk2k98jfw200000gn/T/com.microsoft.Word/WebArchiveCopyPasteTempFiles/350664RR_Q36_stem.png
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A.
/var/folders/9s/5k_n9ntx3sg2tkk2k98jfw200000gn/T/com.microsoft.Word/WebArchiveCopyPasteTempFiles/350664RR_Q36_tan-x-plus-y-over-2.png
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B.
/var/folders/9s/5k_n9ntx3sg2tkk2k98jfw200000gn/T/com.microsoft.Word/WebArchiveCopyPasteTempFiles/350664RR_Q36_tan-x-minus-y-over-2.png
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C.
/var/folders/9s/5k_n9ntx3sg2tkk2k98jfw200000gn/T/com.microsoft.Word/WebArchiveCopyPasteTempFiles/350664RR_Q36_tan-x-plus-tan-y.png
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D.
/var/folders/9s/5k_n9ntx3sg2tkk2k98jfw200000gn/T/com.microsoft.Word/WebArchiveCopyPasteTempFiles/350664RR_Q36_cot-x-minus-y-over-2.png
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7. Use a calculator to solve the equation on the on the interval [0, 2π). Round the answer to two decimal places.
cos x = 0.65
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A. 0.86, 2.28
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B. 0.86, 5.42
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C. 0.86, 4.00
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D. 0.86, 2.43
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8. Find the exact value of the expression:
sin 10° cos 50° + cos 10° sin 50°
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A.
/var/folders/9s/5k_n9ntx3sg2tkk2k98jfw200000gn/T/com.microsoft.Word/WebArchiveCopyPasteTempFiles/350664RR_Q12_1-over-6.png
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B.
/var/folders/9s/5k_n9ntx3sg2tkk2k98jfw200000gn/T/com.microsoft.Word/WebArchiveCopyPasteTempFiles/350664RR_Q12_sqrt3-over-3.png
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C.
/var/folders/9s/5k_n9ntx3sg2tkk2k98jfw200000gn/T/com.microsoft.Word/WebArchiveCopyPasteTempFiles/350664RR_Q12_1-over-2.png
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D.
/var/folders/9s/5k_n9ntx3sg2tkk2k98jfw200000gn/T/com.microsoft.Word/WebArchiveCopyPasteTempFiles/350664RR_sqrt3-over-2.png
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9. Complete the following identity:
(sin x + cos x)2 = _______
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A. 1 + cot 2x
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B. 1 + cos 2x
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C. 1 + sin 2x
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D. 1 + tan 2x
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10. Find the exact value of the expression:
/var/folders/9s/5k_n9ntx3sg2tkk2k98jfw200000gn/T/com.microsoft.Word/WebArchiveCopyPasteTempFiles/350664RR_Q7_stem.png
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A.
/var/folders/9s/5k_n9ntx3sg2tkk2k98jfw200000gn/T/com.microsoft.Word/WebArchiveCopyPasteTempFiles/350664RR_sqrt3-over-2.png
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B.
/var/folders/9s/5k_n9ntx3sg2tkk2k98jfw200000gn/T/com.microsoft.Word/WebArchiveCopyPasteTempFiles/350664RR_minus-sqrt3-over-2.png
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C.
/var/folders/9s/5k_n9ntx3sg2tkk2k98jfw200000gn/T/com.microsoft.Word/WebArchiveCopyPasteTempFiles/350664RR_minus-1-over-2.png
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D.
/var/folders/9s/5k_n9ntx3sg2tkk2k98jfw200000gn/T/com.microsoft.Word/WebArchiveCopyPasteTempFiles/350664RR_Q7_minus-53-over-12.png
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11. Show that the following equation is not an identity by finding a value of x for which both sides are defined but not equal.
cos( x + π) = cos x
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A. 3π ⁄2
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B. 0
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C.
π ⁄2
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D. –π ⁄2
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12. Express the following sum or difference as a product:
sin 8x + sin 4x
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A. 2 sin 6x cos 2x
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B. 2 sin 6x sin 2x
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C. 2 sin 12x
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D. 2 cos 6x sin 2x
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13. Use the graph to complete the identity:
/var/folders/9s/5k_n9ntx3sg2tkk2k98jfw200000gn/T/com.microsoft.Word/WebArchiveCopyPasteTempFiles/350664RR_Q5_stem.png
/var/folders/9s/5k_n9ntx3sg2tkk2k98jfw200000gn/T/com.microsoft.Word/WebArchiveCopyPasteTempFiles/350664RR_Q5_stem_graph.png
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A. cos x
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B. sec x
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C. csc x
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D. sin x
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14. Find all solutions to the following equation:
2 sin x + 1 = 0
2 sin x + 1 = 0
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A.
/var/folders/9s/5k_n9ntx3sg2tkk2k98jfw200000gn/T/com.microsoft.Word/WebArchiveCopyPasteTempFiles/350664RR_Q42_7pi-plus-2npi.png
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B.
/var/folders/9s/5k_n9ntx3sg2tkk2k98jfw200000gn/T/com.microsoft.Word/WebArchiveCopyPasteTempFiles/350664RR_Q42_pi-plus-2npi.png
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C.
/var/folders/9s/5k_n9ntx3sg2tkk2k98jfw200000gn/T/com.microsoft.Word/WebArchiveCopyPasteTempFiles/350664RR_Q42_pi-plus-npi.png
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D.
/var/folders/9s/5k_n9ntx3sg2tkk2k98jfw200000gn/T/com.microsoft.Word/WebArchiveCopyPasteTempFiles/350664RR_Q42_7pi-plus-npi.png
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15. Rewrite the expression in terms of the given function:
(sec x + csc x )(sin x + cos x) – 2 – tan x; cot x
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A. 0
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B. cot x
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C. 2 + cot x
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D. 2cot x
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16. Complete the identity:
tan x (cot x – cos x) = _______
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A. 1
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B. 0
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C. –sec2 x
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D. 1 – sin x
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17. Use a half-angle formula to find the exact value of the following expression:
cos 112.5°
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A.
/var/folders/9s/5k_n9ntx3sg2tkk2k98jfw200000gn/T/com.microsoft.Word/WebArchiveCopyPasteTempFiles/350664RR_Q23_minus-1-over-2-minus-sqrt3.png
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B.
/var/folders/9s/5k_n9ntx3sg2tkk2k98jfw200000gn/T/com.microsoft.Word/WebArchiveCopyPasteTempFiles/350664RR_Q23_1-over-2-minus.png
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C.
/var/folders/9s/5k_n9ntx3sg2tkk2k98jfw200000gn/T/com.microsoft.Word/WebArchiveCopyPasteTempFiles/350664RR_Q23_minus-1-over-2-minus.png
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D.
/var/folders/9s/5k_n9ntx3sg2tkk2k98jfw200000gn/T/com.microsoft.Word/WebArchiveCopyPasteTempFiles/350664RR_Q23_minus-1-over-2-plus.png
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18. Use a calculator to solve the equation on the on the interval [0, 2π). Round to the nearest hundredth of a radian.
sin 3x = –sinx
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A. 1.57, 4.71
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B. 0, 3.14
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C. 0, 0.79, 2.36, 3.14, 3.93, 5.50
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D. 0, 1.57, 3.14, 4.71
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19. Complete the following identity. /var/folders/9s/5k_n9ntx3sg2tkk2k98jfw200000gn/T/com.microsoft.Word/WebArchiveCopyPasteTempFiles/350664RR_Q59_stem.png
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A. sec2 x
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B. cot2 x
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C. 1
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D. csc2 x
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20. Find the exact value of the expression:
cos (165°) cos (45°) + sin (165°) sin (45°)
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A.
/var/folders/9s/5k_n9ntx3sg2tkk2k98jfw200000gn/T/com.microsoft.Word/WebArchiveCopyPasteTempFiles/350664RR_sqrt3-over-2.png
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B.
/var/folders/9s/5k_n9ntx3sg2tkk2k98jfw200000gn/T/com.microsoft.Word/WebArchiveCopyPasteTempFiles/350664RR_minus-1-over-2.png
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C.
/var/folders/9s/5k_n9ntx3sg2tkk2k98jfw200000gn/T/com.microsoft.Word/WebArchiveCopyPasteTempFiles/350664RR_Q8_minus-2.png
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D.
/var/folders/9s/5k_n9ntx3sg2tkk2k98jfw200000gn/T/com.microsoft.Word/WebArchiveCopyPasteTempFiles/350664RR_minus-sqrt3-over-2.png
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