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### Transcript of T RIGONOMETRY Final Review. 1. A PPROXIMATE SEC 320°.77.90 1.1 1.3

• Slide 1
• T RIGONOMETRY Final Review
• Slide 2
• 1. A PPROXIMATE SEC 320.77.90 1.1 1.3
• Slide 3
• T RY AGAIN
• Slide 4
• E XCELLENT !
• Slide 5
• 2. I F SEC =2 FIND TAN . 3/2 3 2
• Slide 6
• T RY AGAIN
• Slide 7
• F ABULOUS !
• Slide 8
• 3. F IND TAN 7 /4.10 -.10 1
• Slide 9
• T RY A GAIN
• Slide 10
• G REAT J OB !
• Slide 11
• 4. F IND A POSITIVE AND NEGATIVE ANGLE COTERMINAL TO 5 /3 ( IN RADIANS ). -11/3 and /3 -/3 and 11/3 -11/3 and 11/3 -/3 and /3
• Slide 12
• T RY A GAIN
• Slide 13
• W AY TO G O !
• Slide 14
• 5. F IND THE REFERENCE ANGLE FOR 13 /6. /6 or 30 /3 or 60 -/6 or -30 -/3 or -60
• Slide 15
• T RY A GAIN
• Slide 16
• R OCK ON !
• Slide 17
• 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
• Slide 18
• T RY AGAIN
• Slide 19
• W OW !
• Slide 20
• 7. F IND 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
• Slide 21
• T RY AGAIN !
• Slide 22
• S UPER !
• Slide 23
• 8. a=4 b=3 and c=5. Find A..64 degrees.93 degrees 36.9 degrees 53.1 degrees
• Slide 24
• T RY AGAIN !
• Slide 25
• Y OU ROCK !
• Slide 26
• 9. B=3420 C=90 and c=8. Find b. 1.78 4.5 6.6 14.8
• Slide 27
• T RY AGAIN !
• Slide 28
• M AGNIFICENT !
• Slide 29
• 10. A=32 C=90 and b=5. Find a. 2.00 3.12 4.24 8.00
• Slide 30
• T RY AGAIN !
• Slide 31
• M ARVELOUS !
• Slide 32
• 11. A=40 B=80 and c=4. Find b. 1.39 2.97 4.55 6.13
• Slide 33
• T RY AGAIN !
• Slide 34
• O UTSTANDING !
• Slide 35
• 12. S IMPLIFY TAN A COS A sinAcosA cosAtanA sinA tanA
• Slide 36
• T RY AGAIN !
• Slide 37
• A WESOME !
• Slide 38
• 13. S IMPLIFY SINX + COSXTANX. sinxcosx 2cosx 2tanx 2sinx
• Slide 39
• T RY AGAIN !
• Slide 40
• H OORAY !
• Slide 41
• 14. S IMPLIFY TANXCSCX sinx cosx secx cotx
• Slide 42
• T RY AGAIN !
• Slide 43
• G REAT JOB !
• Slide 44
• 15. W HICH ONE IS EQUIVALENT TO 1+ TAN SEC 1+csc 1+cot 2sin cos 2sin cos sin +cos
• Slide 45
• T RY AGAIN !
• Slide 46
• W AY TO GO !
• Slide 47
• 16. W HICH IS EQUIVALENT TO 1+ SEC XSIN X cscx secx tanx cotx
• Slide 48
• T RY AGAIN !
• Slide 49
• G REAT JOB !
• Slide 50
• 17. F IND THE DOMAIN AND RANGE FOR Y = CSCX Domain: all reals not equal to k; Range: (-,- 1][1,) Domain: (-,-1][1,); Range: all reals not equal to k Domain: all reals; Range: [-1,1] Domain: all reals not equal to /2+k; Range: (- ,-1][1,)
• Slide 51
• T RY A GAIN !
• Slide 52
• O UTSTANDING !
• Slide 53
• 18. N AME THE AMPLITUDE AND PERIOD AND PHASE SHIFT FOR Y = COS (2 + ) Amplitude: 2, period: , and phase shift /2 right Amplitude: 2, period: /2, and phase shift /2 left Amplitude: 1, period: /2, and phase shift /2 right Amplitude: 1, period: , and phase shift /2 left
• Slide 54
• T RY AGAIN !
• Slide 55
• K EEP UP THE GREAT WORK !
• Slide 56
• 19. N AME THE PERIOD AND PHASE SHIFT FOR Y = TAN ( - /2) Period and phase shift /2 right Period and phase shift /2 left Period 2 and phase shift /2 right Period 2 and phase shift /2 left
• Slide 57
• T RY AGAIN !
• Slide 58
• R IGHT ON !
• Slide 59
• 20. N AME THE AMPLITUDE AND PERIOD AND PHASE SHIFT FOR Y =-3 COS (4 X + /2) Amplitude 3, period /4, and phase shift /2 left Amplitude 3, period /4, and phase shift /8 left Amplitude 3, period /2, and phase shift /2 left Amplitude 3, period /2, and phase shift /8 left
• Slide 60
• T RY AGAIN !
• Slide 61
• S O PROUD OF YOU !
• Slide 62
• 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 units 138.7 units 7947.5 units 10,021.8 units
• Slide 63
• T RY AGAIN
• Slide 64
• E XCELLENT !
• Slide 65
• 22. F IND ALL VALUES OF X WHERE SIN X = 1. 270 + 360k 180 + 360k 90 +360k 360k
• Slide 66
• T RY AGAIN
• Slide 67
• F ABULOUS !
• Slide 68
• 23. E VALUATE COS ( SIN -1 1/2). A SSUME X IS IN QUADRANT 1. (3)/2 3 2 (3)/3
• Slide 69
• T RY AGAIN
• Slide 70
• G REAT J OB !
• Slide 71
• 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
• Slide 72
• T RY AGAIN
• Slide 73
• W AY TO G O !
• Slide 74
• 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
• Slide 75
• T RY AGAIN
• Slide 76
• R OCK ON !
• Slide 77
• 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 /2) Y= 5 cos (2/3x + /2) Y= 5 cos (1/2x /4) Y= 5 cos (1/2x + /4)
• Slide 78
• T RY AGAIN
• Slide 79
• W OW !
• Slide 80
• 27. E XPRESS COS 510 AS A FUNCTION OF AN ANGLE IN QUADRANT I -cos 30 cos 30 -cos 60 cos 60
• Slide 81
• T RY AGAIN
• Slide 82
• G REAT JOB !
• Slide 83
• 28. W HICH EQUATION IS A TRIG IDENTITY ? cos
• Slide 84