11 x1 t08 06 trig equations (2012)
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Transcript of 11 x1 t08 06 trig equations (2012)
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Trig Equations
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Trig Equations 1e.g. i cos 2
2 0 360
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Trig Equations 1e.g. i cos 2
2 0 360
0 2 720
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Trig Equations 1e.g. i cos 2
2 0 360
Q1, Q4 0 2 720
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Trig Equations 1e.g. i cos 2
2 0 360
Q1, Q4
0 2 720
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Trig Equations 1e.g. i cos 2
2 0 360
Q1, Q4
1cos260
0 2 720
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Trig Equations 1e.g. i cos 2
2 0 360
Q1, Q4
1cos260
2 ,360
2 60 ,360 602 60 ,300 ,420 ,660
0 2 720
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Trig Equations 1e.g. i cos 2
2 0 360
Q1, Q4
1cos260
2 ,360
2 60 ,360 602 60 ,300 ,420 ,660
0 2 720
30 ,150 ,210 ,330
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Trig Equations 1e.g. i cos 2
2 0 360
Q1, Q4
1cos260
2 ,360
2 60 ,360 602 60 ,300 ,420 ,660
0 2 720
30 ,150 ,210 ,330
OR 1cos 22
0 360
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Trig Equations 1e.g. i cos 2
2 0 360
Q1, Q4
1cos260
2 ,360
2 60 ,360 602 60 ,300 ,420 ,660
0 2 720
30 ,150 ,210 ,330
OR 1cos 22
0 360
2 12cos 12
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Trig Equations 1e.g. i cos 2
2 0 360
Q1, Q4
1cos260
2 ,360
2 60 ,360 602 60 ,300 ,420 ,660
0 2 720
30 ,150 ,210 ,330
OR 1cos 22
0 360
2 12cos 12
2 3cos4
3cos2
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Trig Equations 1e.g. i cos 2
2 0 360
Q1, Q4
1cos260
2 ,360
2 60 ,360 602 60 ,300 ,420 ,660
0 2 720
30 ,150 ,210 ,330
OR 1cos 22
0 360
2 12cos 12
2 3cos4
3cos2
Q1, Q2, Q3, Q4
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Trig Equations 1e.g. i cos 2
2 0 360
Q1, Q4
1cos260
2 ,360
2 60 ,360 602 60 ,300 ,420 ,660
0 2 720
30 ,150 ,210 ,330
OR 1cos 22
0 360
2 12cos 12
2 3cos4
3cos2
Q1, Q2, Q3, Q4
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Trig Equations 1e.g. i cos 2
2 0 360
Q1, Q4
1cos260
2 ,360
2 60 ,360 602 60 ,300 ,420 ,660
0 2 720
30 ,150 ,210 ,330
OR 1cos 22
0 360
2 12cos 12
2 3cos4
3cos2
Q1, Q2, Q3, Q43cos
230
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Trig Equations 1e.g. i cos 2
2 0 360
Q1, Q4
1cos260
2 ,360
2 60 ,360 602 60 ,300 ,420 ,660
0 2 720
30 ,150 ,210 ,330
OR 1cos 22
0 360
2 12cos 12
2 3cos4
3cos2
Q1, Q2, Q3, Q43cos
230
,180 ,180 ,360
30 ,180 30 ,180 30 ,360 3030 ,150 ,210 ,330
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2ii 4sec 3tan 5x x 0 360x
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2ii 4sec 3tan 5x x 0 360x
2
2
4 4 tan 3tan 54 tan 3tan 1 0
x xx x
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2ii 4sec 3tan 5x x 0 360x
2
2
4 4 tan 3tan 54 tan 3tan 1 0
x xx x
4 tan 1 tan 1 0x x
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2ii 4sec 3tan 5x x 0 360x
2
2
4 4 tan 3tan 54 tan 3tan 1 0
x xx x
4 tan 1 tan 1 0x x 1tan or tan 14
x x
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2ii 4sec 3tan 5x x 0 360x
2
2
4 4 tan 3tan 54 tan 3tan 1 0
x xx x
4 tan 1 tan 1 0x x 1tan or tan 14
x x
Q2, Q4
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2ii 4sec 3tan 5x x 0 360x
2
2
4 4 tan 3tan 54 tan 3tan 1 0
x xx x
4 tan 1 tan 1 0x x 1tan or tan 14
x x
Q2, Q4
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2ii 4sec 3tan 5x x 0 360x
2
2
4 4 tan 3tan 54 tan 3tan 1 0
x xx x
4 tan 1 tan 1 0x x 1tan or tan 14
x x
Q2, Q41tan414 2
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2ii 4sec 3tan 5x x 0 360x
2
2
4 4 tan 3tan 54 tan 3tan 1 0
x xx x
4 tan 1 tan 1 0x x 1tan or tan 14
x x
Q2, Q41tan414 2
180 ,360x
180 14 2 ,360 14 2165 58 ,345 58
xx
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2ii 4sec 3tan 5x x 0 360x
2
2
4 4 tan 3tan 54 tan 3tan 1 0
x xx x
4 tan 1 tan 1 0x x 1tan or tan 14
x x
Q2, Q41tan414 2
180 ,360x
180 14 2 ,360 14 2165 58 ,345 58
xx
Q1, Q3
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2ii 4sec 3tan 5x x 0 360x
2
2
4 4 tan 3tan 54 tan 3tan 1 0
x xx x
4 tan 1 tan 1 0x x 1tan or tan 14
x x
Q2, Q41tan414 2
180 ,360x
180 14 2 ,360 14 2165 58 ,345 58
xx
Q1, Q3
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2ii 4sec 3tan 5x x 0 360x
2
2
4 4 tan 3tan 54 tan 3tan 1 0
x xx x
4 tan 1 tan 1 0x x 1tan or tan 14
x x
Q2, Q41tan414 2
180 ,360x
180 14 2 ,360 14 2165 58 ,345 58
xx
Q1, Q3
tan 145
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2ii 4sec 3tan 5x x 0 360x
2
2
4 4 tan 3tan 54 tan 3tan 1 0
x xx x
4 tan 1 tan 1 0x x 1tan or tan 14
x x
Q2, Q41tan414 2
180 ,360x
180 14 2 ,360 14 2165 58 ,345 58
xx
Q1, Q3
tan 145
,180x
45 ,180 4545 ,225
xx
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2ii 4sec 3tan 5x x 0 360x
2
2
4 4 tan 3tan 54 tan 3tan 1 0
x xx x
4 tan 1 tan 1 0x x 1tan or tan 14
x x
Q2, Q41tan414 2
180 ,360x
180 14 2 ,360 14 2165 58 ,345 58
xx
Q1, Q3
tan 145
,180x
45 ,180 4545 ,225
xx
45 ,165 58 ,225 ,345 58x
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2 2iii cos 2 4cos 2sin 0 360
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2 2iii cos 2 4cos 2sin 0 360
2 2 2 2cos sin 4cos 2sin
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2 2iii cos 2 4cos 2sin 0 360
2 2 2 2cos sin 4cos 2sin 2 23cos sin
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2 2iii cos 2 4cos 2sin 0 360
2 2 2 2cos sin 4cos 2sin 2 23cos sin 2tan 3
tan 3
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2 2iii cos 2 4cos 2sin 0 360
2 2 2 2cos sin 4cos 2sin 2 23cos sin 2tan 3
tan 3
Q1, Q2, Q3, Q4
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2 2iii cos 2 4cos 2sin 0 360
2 2 2 2cos sin 4cos 2sin 2 23cos sin 2tan 3
tan 3
Q1, Q2, Q3, Q4
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2 2iii cos 2 4cos 2sin 0 360
2 2 2 2cos sin 4cos 2sin 2 23cos sin 2tan 3
tan 3
Q1, Q2, Q3, Q4
tan 360
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2 2iii cos 2 4cos 2sin 0 360
2 2 2 2cos sin 4cos 2sin 2 23cos sin 2tan 3
tan 3
Q1, Q2, Q3, Q4
tan 360
,180 ,180 ,360
60 ,180 60 ,180 60 ,360 6060 ,120 ,240 ,300
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2 2iii cos 2 4cos 2sin 0 360
2 2 2 2cos sin 4cos 2sin 2 23cos sin 2tan 3
tan 3
Q1, Q2, Q3, Q4
tan 360
,180 ,180 ,360
60 ,180 60 ,180 60 ,360 6060 ,120 ,240 ,300
2000 Extension 1 HSC Q2c)(iv) cos 2 sin , 0 360
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2 2iii cos 2 4cos 2sin 0 360
2 2 2 2cos sin 4cos 2sin 2 23cos sin 2tan 3
tan 3
Q1, Q2, Q3, Q4
tan 360
,180 ,180 ,360
60 ,180 60 ,180 60 ,360 6060 ,120 ,240 ,300
2000 Extension 1 HSC Q2c)(iv) cos 2 sin , 0 360
sinsin21 2
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2 2iii cos 2 4cos 2sin 0 360
2 2 2 2cos sin 4cos 2sin 2 23cos sin 2tan 3
tan 3
Q1, Q2, Q3, Q4
tan 360
,180 ,180 ,360
60 ,180 60 ,180 60 ,360 6060 ,120 ,240 ,300
2000 Extension 1 HSC Q2c)(iv) cos 2 sin , 0 360
sinsin21 2 01sinsin2 2
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2 2iii cos 2 4cos 2sin 0 360
2 2 2 2cos sin 4cos 2sin 2 23cos sin 2tan 3
tan 3
Q1, Q2, Q3, Q4
tan 360
,180 ,180 ,360
60 ,180 60 ,180 60 ,360 6060 ,120 ,240 ,300
2000 Extension 1 HSC Q2c)(iv) cos 2 sin , 0 360
sinsin21 2 01sinsin2 2
01sin1sin2
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2 2iii cos 2 4cos 2sin 0 360
2 2 2 2cos sin 4cos 2sin 2 23cos sin 2tan 3
tan 3
Q1, Q2, Q3, Q4
tan 360
,180 ,180 ,360
60 ,180 60 ,180 60 ,360 6060 ,120 ,240 ,300
2000 Extension 1 HSC Q2c)(iv) cos 2 sin , 0 360
sinsin21 2 01sinsin2 2
01sin1sin2
1sinor 21sin
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2 2iii cos 2 4cos 2sin 0 360
2 2 2 2cos sin 4cos 2sin 2 23cos sin 2tan 3
tan 3
Q1, Q2, Q3, Q4
tan 360
,180 ,180 ,360
60 ,180 60 ,180 60 ,360 6060 ,120 ,240 ,300
2000 Extension 1 HSC Q2c)(iv) cos 2 sin , 0 360
sinsin21 2 01sinsin2 2
01sin1sin2
1sinor 21sin
Q1, Q2
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2 2iii cos 2 4cos 2sin 0 360
2 2 2 2cos sin 4cos 2sin 2 23cos sin 2tan 3
tan 3
Q1, Q2, Q3, Q4
tan 360
,180 ,180 ,360
60 ,180 60 ,180 60 ,360 6060 ,120 ,240 ,300
2000 Extension 1 HSC Q2c)(iv) cos 2 sin , 0 360
sinsin21 2 01sinsin2 2
01sin1sin2
1sinor 21sin
Q1, Q2
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2 2iii cos 2 4cos 2sin 0 360
2 2 2 2cos sin 4cos 2sin 2 23cos sin 2tan 3
tan 3
Q1, Q2, Q3, Q4
tan 360
,180 ,180 ,360
60 ,180 60 ,180 60 ,360 6060 ,120 ,240 ,300
2000 Extension 1 HSC Q2c)(iv) cos 2 sin , 0 360
sinsin21 2 01sinsin2 2
01sin1sin2
1sinor 21sin
Q1, Q2 270
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2 2iii cos 2 4cos 2sin 0 360
2 2 2 2cos sin 4cos 2sin 2 23cos sin 2tan 3
tan 3
Q1, Q2, Q3, Q4
tan 360
,180 ,180 ,360
60 ,180 60 ,180 60 ,360 6060 ,120 ,240 ,300
2000 Extension 1 HSC Q2c)(iv) cos 2 sin , 0 360
sinsin21 2 01sinsin2 2
01sin1sin2
1sinor 21sin
Q1, Q2 270
3021sin
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2 2iii cos 2 4cos 2sin 0 360
2 2 2 2cos sin 4cos 2sin 2 23cos sin 2tan 3
tan 3
Q1, Q2, Q3, Q4
tan 360
,180 ,180 ,360
60 ,180 60 ,180 60 ,360 6060 ,120 ,240 ,300
2000 Extension 1 HSC Q2c)(iv) cos 2 sin , 0 360
sinsin21 2 01sinsin2 2
01sin1sin2
1sinor 21sin
Q1, Q2 270
3021sin
,180
30 ,180 3030 ,150
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2 2iii cos 2 4cos 2sin 0 360
2 2 2 2cos sin 4cos 2sin 2 23cos sin 2tan 3
tan 3
Q1, Q2, Q3, Q4
tan 360
,180 ,180 ,360
60 ,180 60 ,180 60 ,360 6060 ,120 ,240 ,300
2000 Extension 1 HSC Q2c)(iv) cos 2 sin , 0 360
sinsin21 2 01sinsin2 2
01sin1sin2
1sinor 21sin
Q1, Q2 270
3021sin
,180
30 ,180 3030 ,150
270,150,30
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1992 Extension 1 HSC Q2a)2(v) 2sin sin 2 , 0 360
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1992 Extension 1 HSC Q2a)2(v) 2sin sin 2 , 0 360
cossin2sin2 2
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1992 Extension 1 HSC Q2a)2(v) 2sin sin 2 , 0 360
cossin2sin2 2
0cossin2sin2 2
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1992 Extension 1 HSC Q2a)2(v) 2sin sin 2 , 0 360
cossin2sin2 2
0cossin2sin2 2
0cossinsin2
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1992 Extension 1 HSC Q2a)2(v) 2sin sin 2 , 0 360
cossin2sin2 2
0cossin2sin2 2
sin 0 or sin cos
0cossinsin2
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1992 Extension 1 HSC Q2a)2(v) 2sin sin 2 , 0 360
cossin2sin2 2
0cossin2sin2 2
sin 0 or sin cos
0cossinsin2
360,180,0
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1992 Extension 1 HSC Q2a)2(v) 2sin sin 2 , 0 360
cossin2sin2 2
0cossin2sin2 2
sin 0 or sin cos
0cossinsin2
360,180,0 1tan
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1992 Extension 1 HSC Q2a)2(v) 2sin sin 2 , 0 360
cossin2sin2 2
0cossin2sin2 2
sin 0 or sin cos
0cossinsin2
360,180,0 1tan Q1, Q3
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1992 Extension 1 HSC Q2a)2(v) 2sin sin 2 , 0 360
cossin2sin2 2
0cossin2sin2 2
sin 0 or sin cos
0cossinsin2
360,180,0 1tan Q1, Q3
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1992 Extension 1 HSC Q2a)2(v) 2sin sin 2 , 0 360
cossin2sin2 2
0cossin2sin2 2
sin 0 or sin cos
0cossinsin2
360,180,0 1tan Q1, Q3
tan 145
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1992 Extension 1 HSC Q2a)2(v) 2sin sin 2 , 0 360
cossin2sin2 2
0cossin2sin2 2
sin 0 or sin cos
0cossinsin2
360,180,0 1tan Q1, Q3
tan 145
,180
45 ,180 4545 ,225
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1992 Extension 1 HSC Q2a)2(v) 2sin sin 2 , 0 360
cossin2sin2 2
0cossin2sin2 2
sin 0 or sin cos
0cossinsin2
360,180,0 1tan Q1, Q3
tan 145
,180
45 ,180 4545 ,225
360,225,180,45,0
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1992 Extension 1 HSC Q2a)2(v) 2sin sin 2 , 0 360
cossin2sin2 2
0cossin2sin2 2
sin 0 or sin cos
0cossinsin2
360,180,0 1tan Q1, Q3
tan 145
,180
45 ,180 4545 ,225
360,225,180,45,0
Exercise 2D;2ac, 4ac, 5adgi,9adgj, 10bdfij,
16, 24*