T RIGONOMETRY Final Review
1. A PPROXIMATE SEC 320°
T RY AGAIN
E XCELLENT !
2. I F SEC =2 FIND TAN . √3/2 ½ √3 2
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F ABULOUS !
3. F IND TAN 7 Π /
T RY A GAIN
G REAT J OB !
4. F IND A POSITIVE AND NEGATIVE ANGLE COTERMINAL TO 5 Π /3 ( IN RADIANS ). -11π/3 and π/3 -π/3 and 11π/3 -11π/3 and 11π/3 -π/3 and π/3
T RY A GAIN
W AY TO G O !
5. F IND THE REFERENCE ANGLE FOR 13 Π /6. π/6 or 30° π/3 or 60° -π/6 or -30° -π/3 or -60°
T RY A GAIN
R OCK ON !
6. F IND 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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W OW !
7. F IND THE APPROXIMATE ARC LENGTH IF THE CENTRAL ANGLE IS 40° AND THE RADIUS OF THE CIRCLE BEING INTERCEPTED IS 5 UNITS
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S UPER !
8. a=4 b=3 and c=5. Find A..64 degrees.93 degrees 36.9 degrees 53.1 degrees
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Y OU ROCK !
9. B=34°20’ C=90° and c=8. Find b
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M AGNIFICENT !
10. A=32° C=90° and b=5. Find a
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M ARVELOUS !
11. A=40° B=80° and c=4. Find b
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O UTSTANDING !
12. S IMPLIFY TAN A COS ²A sinAcosA cosAtanA sin²A tan²A
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A WESOME !
13. S IMPLIFY SINX + COSXTANX. sinxcosx 2cosx 2tanx 2sinx
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H OORAY !
14. S IMPLIFY TANXCSCX sinx cosx secx cotx
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G REAT JOB !
15. W HICH ONE IS EQUIVALENT TO 1+ TAN SEC 1+csc 1+cot 2sin cos 2sin cos sin +cos
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W AY TO GO !
16. W HICH IS EQUIVALENT TO 1+ SEC ² XSIN ² X csc²x sec²x tan²x cot²x
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G REAT JOB !
17. F IND 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+πk; Range: (- ∞,-1][1,∞)
T RY A GAIN !
O UTSTANDING !
18. N AME 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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K EEP UP THE GREAT WORK !
19. N AME 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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R IGHT ON !
20. N AME THE AMPLITUDE AND PERIOD AND PHASE SHIFT FOR Y =-3 COS (4 X + 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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S O PROUD OF YOU !
21. F IND 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 units² units² 10,021.8 units²
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E XCELLENT !
22. F IND ALL VALUES OF X WHERE SIN X = ° + 360k 180° + 360k 90° +360k 360k
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F ABULOUS !
23. E VALUATE COS ( SIN -1 1/2). A SSUME X IS IN QUADRANT 1. √(3)/2 √3 2 √(3)/3
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G REAT J OB !
24. F IND 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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W AY TO G O !
25. E VALUATE COS ( TAN -1 1) + SIN ( TAN -1 √3) ( X IS IN Q UADRANT I) 1 + √(3)/2 2 + √(2)/2 √(2)/2 + √(3)/2 √(3)/3 + √3
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R OCK ON !
26. W RITE 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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W OW !
27. E XPRESS COS 510˚ AS A FUNCTION OF AN ANGLE IN QUADRANT I -cos 30˚ cos 30˚ -cos 60˚ cos 60˚
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G REAT JOB !
28. W HICH EQUATION IS A TRIG IDENTITY ? cos