t rigonometry final review. 1. a pproximate sec 320°.77.90 1.1 1.3
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TRIGONOMETRYFinal Review
1. APPROXIMATE SEC 320°
.77 .90 1.1 1.3
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EXCELLENT!
2. IF SEC =2 FIND TAN .
√3/2 ½ √3 2
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FABULOUS!
3. FIND TAN 7Π/4
.10 -.10 1 -1
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GREAT JOB!
4. FIND A POSITIVE AND NEGATIVE ANGLE COTERMINAL TO 5Π/3 (IN RADIANS).
-11π/3 and π/3 -π/3 and 11π/3 -11π/3 and 11π/3 -π/3 and π/3
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WAY TO GO!
5. FIND THE REFERENCE ANGLE FOR 13Π/6.
π/6 or 30° π/3 or 60° -π/6 or -30° -π/3 or -60°
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ROCK ON!
6. FIND ALL VALUES BETWEEN 0 AND 360° WHERE SIN =-1/2
150° and 210° 240° and 320° 210° and 330° 150° and 330°
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WOW!
7. FIND THE APPROXIMATE ARC LENGTH IF THE CENTRAL ANGLE IS 40° AND THE RADIUS OF THE CIRCLE BEING INTERCEPTED IS 5 UNITS.
1.75 3.49 5.25 200
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SUPER!
8. a=4 b=3 and c=5. Find A.
.64 degrees .93 degrees 36.9 degrees 53.1 degrees
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YOU ROCK!
9. B=34°20’ C=90° and c=8. Find b.
1.78 4.5 6.6 14.8
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MAGNIFICENT!
10. A=32° C=90° and b=5. Find a.
2.00 3.12 4.24 8.00
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MARVELOUS!
11. A=40° B=80° and c=4. Find b.
1.39 2.97 4.55 6.13
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OUTSTANDING!
12. SIMPLIFY TANACOS²A
sinAcosA cosAtanA sin²A tan²A
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AWESOME!
13. SIMPLIFY SINX+COSXTANX.
sinxcosx 2cosx 2tanx 2sinx
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HOORAY!
14. SIMPLIFY TANXCSCX
sinx cosx secx cotx
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GREAT JOB!
15. WHICH ONE IS EQUIVALENT TO 1+TAN SEC
1+csc 1+cot 2sincos sin+cos
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WAY TO GO!
16. WHICH IS EQUIVALENT TO 1+SEC²XSIN²X
csc²x sec²x tan²x cot²x
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GREAT JOB!
17. FIND THE DOMAIN AND RANGE FOR Y=CSCX
Domain: all reals not equal to πk; Range: (-∞,-1][1,∞)
Domain: (-∞,-1][1,∞); Range: all reals not equal to πk
Domain: all reals; Range: [-1,1] Domain: all reals not equal to π/2+π
k; Range: (-∞,-1][1,∞)
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OUTSTANDING!
18. NAME THE AMPLITUDE AND PERIOD AND PHASE SHIFT FOR Y=COS(2+Π)
Amplitude: 2, period: π, and phase shift π/2 right
Amplitude: 2, period: π/2, and phase shift π/2 left
Amplitude: 1, period: π/2, and phase shift π/2 right
Amplitude: 1, period: π, and phase shift π/2 left
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KEEP UP THE GREAT WORK!
19. NAME THE PERIOD AND PHASE SHIFT FOR Y= TAN(-Π/2)
Period π and phase shift π/2 right Period π and phase shift π/2 left Period 2π and phase shift π/2 right Period 2π and phase shift π/2 left
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RIGHT ON!
20. NAME THE AMPLITUDE AND PERIOD AND PHASE SHIFT FOR Y=-3COS(4X+Π/2)
Amplitude 3, period π/4, and phase shift π/2 left
Amplitude 3, period π/4, and phase shift π/8 left
Amplitude 3, period π/2, and phase shift π/2 left
Amplitude 3, period π/2, and phase shift π/8 left
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SO PROUD OF YOU!
21. FIND THE AREA OF A CIRCULAR SEGMENT TO THE NEAREST TENTH IF THE MEASURE OF ITS CENTRAL ANGLE IS 220° AND THE MEASURE OF ITS RADIUS IS 8.5 UNITS.
935 units² 138.7 units² 7947.5 units² 10,021.8 units²
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EXCELLENT!
22. FIND ALL VALUES OF X WHERE SIN X = 1.
270° + 360k 180° + 360k 90° +360k 360k
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FABULOUS!
23. EVALUATE COS(SIN-11/2). ASSUME X IS IN QUADRANT 1.
√(3)/2 √3 2 √(3)/3
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GREAT JOB!
24. FIND THE VALUES OF X IN THE INTERVAL [-180˚, 180˚] THAT SATISFY THE EQUATION SIN X = -1/2.
30˚ and 150˚ 60˚ and 300˚ -60˚ and -300˚ -30˚ and -150˚
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WAY TO GO!
25. EVALUATE COS(TAN-11) + SIN(TAN-1√3)
(X IS IN QUADRANT I)
1 + √(3)/2 2 + √(2)/2 √(2)/2 + √(3)/2 √(3)/3 + √3
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ROCK ON!
26. WRITE AN EQUATION OF THE COSINE FUNCTION WITH AMPLITUDE 5, PERIOD 540˚ AND PHASE SHIFT 135˚ TO THE LEFT.
Y= 5 cos (2/3x – л/2) Y= 5 cos (2/3x + л/2) Y= 5 cos (1/2x – л/4) Y= 5 cos (1/2x + л/4)
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WOW!
27. EXPRESS COS 510˚ AS A FUNCTION OF AN ANGLE IN QUADRANT I
-cos 30˚ cos 30˚ -cos 60˚ cos 60˚
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GREAT JOB!
28. WHICH EQUATION IS A TRIG IDENTITY?
cos
