11x1 t07 07 asinx + bcosx = c (2011)
TRANSCRIPT
![Page 1: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/1.jpg)
Equations of the form asinx + bcosx = cMethod 1: Using the t results
![Page 2: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/2.jpg)
Equations of the form asinx + bcosx = cMethod 1: Using the t results
3600 eg (i) 3cos 4sin 2
![Page 3: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/3.jpg)
Equations of the form asinx + bcosx = cMethod 1: Using the t results
3600 eg (i) 3cos 4sin 2
let tan2
t
![Page 4: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/4.jpg)
Equations of the form asinx + bcosx = cMethod 1: Using the t results
3600 eg (i) 3cos 4sin 2 2
2 21 23 4 2 0 1801 1 2
t tt t
let tan
2t
![Page 5: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/5.jpg)
Equations of the form asinx + bcosx = cMethod 1: Using the t results
3600 eg (i) 3cos 4sin 2 2
2 21 23 4 2 0 1801 1 2
t tt t
let tan
2t
2 23 3 8 2 2t t t
![Page 6: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/6.jpg)
Equations of the form asinx + bcosx = cMethod 1: Using the t results
3600 eg (i) 3cos 4sin 2 2
2 21 23 4 2 0 1801 1 2
t tt t
let tan
2t
2 23 3 8 2 2t t t 25 8 1 0t t
![Page 7: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/7.jpg)
Equations of the form asinx + bcosx = cMethod 1: Using the t results
3600 eg (i) 3cos 4sin 2 2
2 21 23 4 2 0 1801 1 2
t tt t
let tan
2t
2 23 3 8 2 2t t t 25 8 1 0t t
8 8410
t
![Page 8: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/8.jpg)
Equations of the form asinx + bcosx = cMethod 1: Using the t results
3600 eg (i) 3cos 4sin 2 2
2 21 23 4 2 0 1801 1 2
t tt t
let tan
2t
2 23 3 8 2 2t t t 25 8 1 0t t
8 8410
t
4 21 4 21tan or tan2 5 2 5
![Page 9: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/9.jpg)
Equations of the form asinx + bcosx = cMethod 1: Using the t results
3600 eg (i) 3cos 4sin 2 2
2 21 23 4 2 0 1801 1 2
t tt t
let tan
2t
2 23 3 8 2 2t t t 25 8 1 0t t
8 8410
t
4 21 4 21tan or tan2 5 2 5
Q2
![Page 10: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/10.jpg)
Equations of the form asinx + bcosx = cMethod 1: Using the t results
3600 eg (i) 3cos 4sin 2 2
2 21 23 4 2 0 1801 1 2
t tt t
let tan
2t
2 23 3 8 2 2t t t 25 8 1 0t t
8 8410
t
4 21 4 21tan or tan2 5 2 5
Q2 21 4tan5
6 39
![Page 11: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/11.jpg)
Equations of the form asinx + bcosx = cMethod 1: Using the t results
3600 eg (i) 3cos 4sin 2 2
2 21 23 4 2 0 1801 1 2
t tt t
let tan
2t
2 23 3 8 2 2t t t 25 8 1 0t t
8 8410
t
4 21 4 21tan or tan2 5 2 5
Q2 21 4tan5
6 39
173 212
346 42
![Page 12: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/12.jpg)
Equations of the form asinx + bcosx = cMethod 1: Using the t results
3600 eg (i) 3cos 4sin 2 2
2 21 23 4 2 0 1801 1 2
t tt t
let tan
2t
2 23 3 8 2 2t t t 25 8 1 0t t
8 8410
t
4 21 4 21tan or tan2 5 2 5
Q2 21 4tan5
6 39
173 212
346 42
Q1
![Page 13: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/13.jpg)
Equations of the form asinx + bcosx = cMethod 1: Using the t results
3600 eg (i) 3cos 4sin 2 2
2 21 23 4 2 0 1801 1 2
t tt t
let tan
2t
2 23 3 8 2 2t t t 25 8 1 0t t
8 8410
t
4 21 4 21tan or tan2 5 2 5
Q2 21 4tan5
6 39
173 212
346 42
Q1 4 21tan5
59 47
![Page 14: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/14.jpg)
Equations of the form asinx + bcosx = cMethod 1: Using the t results
3600 eg (i) 3cos 4sin 2 2
2 21 23 4 2 0 1801 1 2
t tt t
let tan
2t
2 23 3 8 2 2t t t 25 8 1 0t t
8 8410
t
4 21 4 21tan or tan2 5 2 5
Q2 21 4tan5
6 39
173 212
346 42
Q1 4 21tan5
59 47
59 472
119 33
![Page 15: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/15.jpg)
Equations of the form asinx + bcosx = cMethod 1: Using the t results
3600 eg (i) 3cos 4sin 2 2
2 21 23 4 2 0 1801 1 2
t tt t
let tan
2t
2 23 3 8 2 2t t t 25 8 1 0t t
8 8410
t
4 21 4 21tan or tan2 5 2 5
Q2 21 4tan5
6 39
173 212
346 42
Q1 4 21tan5
59 47
59 472
119 33
180: Test
![Page 16: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/16.jpg)
Equations of the form asinx + bcosx = cMethod 1: Using the t results
3600 eg (i) 3cos 4sin 2 2
2 21 23 4 2 0 1801 1 2
t tt t
let tan
2t
2 23 3 8 2 2t t t 25 8 1 0t t
8 8410
t
4 21 4 21tan or tan2 5 2 5
Q2 21 4tan5
6 39
173 212
346 42
Q1 4 21tan5
59 47
59 472
119 33
180: Test
3cos180 4sin1804 2
![Page 17: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/17.jpg)
Equations of the form asinx + bcosx = cMethod 1: Using the t results
3600 eg (i) 3cos 4sin 2 2
2 21 23 4 2 0 1801 1 2
t tt t
let tan
2t
2 23 3 8 2 2t t t 25 8 1 0t t
8 8410
t
4 21 4 21tan or tan2 5 2 5
Q2 21 4tan5
6 39
173 212
346 42
Q1 4 21tan5
59 47
59 472
119 33
180: Test
3cos180 4sin1804 2
119 33 ,346 42
![Page 18: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/18.jpg)
Method 2: Auxiliary Angle Method(i) Change into a sine functioneg (i) 3cos 4sin 2 3600
![Page 19: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/19.jpg)
Method 2: Auxiliary Angle Method(i) Change into a sine functioneg (i) 3cos 4sin 2 3600
3cos 4sin 2
![Page 20: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/20.jpg)
Method 2: Auxiliary Angle Method(i) Change into a sine functioneg (i) 3cos 4sin 2 3600
3cos 4sin 2
sincoscossin
![Page 21: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/21.jpg)
Method 2: Auxiliary Angle Method(i) Change into a sine functioneg (i) 3cos 4sin 2 3600
3cos 4sin 2
sincoscossin
![Page 22: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/22.jpg)
Method 2: Auxiliary Angle Method(i) Change into a sine functioneg (i) 3cos 4sin 2 3600
3cos 4sin 2
sincoscossin
sin corresponds to 3, so 3 goes on the opposite
side
3
![Page 23: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/23.jpg)
Method 2: Auxiliary Angle Method(i) Change into a sine functioneg (i) 3cos 4sin 2 3600
3cos 4sin 2
sincoscossin
3
![Page 24: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/24.jpg)
Method 2: Auxiliary Angle Method(i) Change into a sine functioneg (i) 3cos 4sin 2 3600
3cos 4sin 2
sincoscossin
3
cos corresponds to 4, so 4 goes on the adjacent
side
4
![Page 25: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/25.jpg)
Method 2: Auxiliary Angle Method(i) Change into a sine functioneg (i) 3cos 4sin 2 3600
3cos 4sin 2
sincoscossin
3
4
by Pythagoras the hypotenuse is 5
5
![Page 26: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/26.jpg)
Method 2: Auxiliary Angle Method(i) Change into a sine functioneg (i) 3cos 4sin 2 3600
3cos 4sin 2
sincoscossin
3
4
by Pythagoras the hypotenuse is 5
5
3 45 cos sin 25 5
![Page 27: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/27.jpg)
Method 2: Auxiliary Angle Method(i) Change into a sine functioneg (i) 3cos 4sin 2 3600
3cos 4sin 2
sincoscossin
3
4
by Pythagoras the hypotenuse is 5
5
5sin 2
3 45 cos sin 25 5
![Page 28: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/28.jpg)
Method 2: Auxiliary Angle Method(i) Change into a sine functioneg (i) 3cos 4sin 2 3600
3cos 4sin 2
sincoscossin
3
4
by Pythagoras the hypotenuse is 5
5
5sin 2
The hypotenuse becomes the coefficient of the trig function
3 45 cos sin 25 5
![Page 29: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/29.jpg)
Method 2: Auxiliary Angle Method(i) Change into a sine functioneg (i) 3cos 4sin 2 3600
3cos 4sin 2
3
4
5
5sin 2
3 45 cos sin 25 5
3tan
4
2sin5
![Page 30: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/30.jpg)
Method 2: Auxiliary Angle Method(i) Change into a sine functioneg (i) 3cos 4sin 2 3600
3cos 4sin 2
3
4
5
5sin 2
3 45 cos sin 25 5
3tan
4
36 52 2sin5
![Page 31: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/31.jpg)
Method 2: Auxiliary Angle Method(i) Change into a sine functioneg (i) 3cos 4sin 2 3600
3cos 4sin 2
3
4
5
5sin 2
3 45 cos sin 25 5
3tan
4
36 52 2sin5
Q1, Q2
![Page 32: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/32.jpg)
Method 2: Auxiliary Angle Method(i) Change into a sine functioneg (i) 3cos 4sin 2 3600
3cos 4sin 2
3
4
5
5sin 2
3 45 cos sin 25 5
3tan
4
36 52 2sin5
Q1, Q2
2sin5
![Page 33: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/33.jpg)
Method 2: Auxiliary Angle Method(i) Change into a sine functioneg (i) 3cos 4sin 2 3600
3cos 4sin 2
3
4
5
5sin 2
3 45 cos sin 25 5
3tan
4
36 52 2sin5
Q1, Q2
2sin5
23 35
![Page 34: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/34.jpg)
Method 2: Auxiliary Angle Method(i) Change into a sine functioneg (i) 3cos 4sin 2 3600
3cos 4sin 2
3
4
5
5sin 2
3 45 cos sin 25 5
3tan
4
36 52 2sin5
Q1, Q2
2sin5
23 35
36 52 23 35 ,156 25
![Page 35: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/35.jpg)
Method 2: Auxiliary Angle Method(i) Change into a sine functioneg (i) 3cos 4sin 2 3600
3cos 4sin 2
3
4
5
5sin 2
3 45 cos sin 25 5
3tan
4
36 52 2sin5
Q1, Q2
2sin5
23 35
36 52 23 35 ,156 25
13 17 ,119 33
![Page 36: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/36.jpg)
Method 2: Auxiliary Angle Method(i) Change into a sine functioneg (i) 3cos 4sin 2 3600
3cos 4sin 2
3
4
5
5sin 2
3 45 cos sin 25 5
3tan
4
36 52 2sin5
Q1, Q2
2sin5
23 35
36 52 23 35 ,156 25 119 33 ,346 43
13 17 ,119 33
![Page 37: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/37.jpg)
Method 2: Auxiliary Angle Method(ii) Change into a cosine functioneg (i) 3cos 4sin 2 3600
![Page 38: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/38.jpg)
Method 2: Auxiliary Angle Method(ii) Change into a cosine functioneg (i) 3cos 4sin 2 3600
3cos 4sin 2
![Page 39: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/39.jpg)
Method 2: Auxiliary Angle Method(ii) Change into a cosine functioneg (i) 3cos 4sin 2 3600
3cos 4sin 2
cos cos sin sin
![Page 40: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/40.jpg)
Method 2: Auxiliary Angle Method(ii) Change into a cosine functioneg (i) 3cos 4sin 2 3600
3cos 4sin 2
cos cos sin sin
![Page 41: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/41.jpg)
Method 2: Auxiliary Angle Method(ii) Change into a cosine functioneg (i) 3cos 4sin 2 3600
3cos 4sin 2
cos cos sin sin
cos corresponds to 3, so 3 goes on the adjacent
side
3
![Page 42: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/42.jpg)
Method 2: Auxiliary Angle Method(ii) Change into a cosine functioneg (i) 3cos 4sin 2 3600
3cos 4sin 2
cos cos sin sin
3
![Page 43: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/43.jpg)
Method 2: Auxiliary Angle Method(ii) Change into a cosine functioneg (i) 3cos 4sin 2 3600
3cos 4sin 2
cos cos sin sin
3
cos corresponds to 4, so 4 goes on the adjacent
side
4
![Page 44: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/44.jpg)
Method 2: Auxiliary Angle Method(ii) Change into a cosine functioneg (i) 3cos 4sin 2 3600
3cos 4sin 2
cos cos sin sin
3
4
by Pythagoras the hypotenuse is 5
5
![Page 45: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/45.jpg)
Method 2: Auxiliary Angle Method(ii) Change into a cosine functioneg (i) 3cos 4sin 2 3600
3cos 4sin 2
cos cos sin sin
3
4
by Pythagoras the hypotenuse is 5
5
3 45 cos sin 25 5
![Page 46: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/46.jpg)
Method 2: Auxiliary Angle Method(ii) Change into a cosine functioneg (i) 3cos 4sin 2 3600
3cos 4sin 2
cos cos sin sin
3
4
by Pythagoras the hypotenuse is 5
5
5cos 2
3 45 cos sin 25 5
![Page 47: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/47.jpg)
Method 2: Auxiliary Angle Method(ii) Change into a cosine functioneg (i) 3cos 4sin 2 3600
3cos 4sin 2
cos cos sin sin
3
4
by Pythagoras the hypotenuse is 5
5
5cos 2
The hypotenuse becomes the coefficient of the trig function
3 45 cos sin 25 5
![Page 48: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/48.jpg)
Method 2: Auxiliary Angle Method(ii) Change into a cosine functioneg (i) 3cos 4sin 2 3600
3cos 4sin 2
cos cos sin sin
3
45
5cos 2
3 45 cos sin 25 5
4tan
3
2cos5
![Page 49: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/49.jpg)
Method 2: Auxiliary Angle Method(ii) Change into a cosine functioneg (i) 3cos 4sin 2 3600
3cos 4sin 2
cos cos sin sin
3
45
5cos 2
3 45 cos sin 25 5
4tan
3
53 8 2cos5
![Page 50: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/50.jpg)
Method 2: Auxiliary Angle Method(ii) Change into a cosine functioneg (i) 3cos 4sin 2 3600
3cos 4sin 2
cos cos sin sin
3
45
5cos 2
3 45 cos sin 25 5
4tan
3
53 8 2cos5
Q1, Q4
![Page 51: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/51.jpg)
Method 2: Auxiliary Angle Method(ii) Change into a cosine functioneg (i) 3cos 4sin 2 3600
3cos 4sin 2
cos cos sin sin
3
45
5cos 2
3 45 cos sin 25 5
4tan
3
53 8 2cos5
Q1, Q4
2cos5
![Page 52: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/52.jpg)
Method 2: Auxiliary Angle Method(ii) Change into a cosine functioneg (i) 3cos 4sin 2 3600
3cos 4sin 2
cos cos sin sin
3
45
5cos 2
3 45 cos sin 25 5
4tan
3
53 8 2cos5
Q1, Q4
2cos5
66 25
![Page 53: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/53.jpg)
Method 2: Auxiliary Angle Method(ii) Change into a cosine functioneg (i) 3cos 4sin 2 3600
3cos 4sin 2
cos cos sin sin
3
45
5cos 2
3 45 cos sin 25 5
4tan
3
53 8 2cos5
Q1, Q4
2cos5
66 25
53 8 66 25 ,293 35
![Page 54: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/54.jpg)
Method 2: Auxiliary Angle Method(ii) Change into a cosine functioneg (i) 3cos 4sin 2 3600
3cos 4sin 2
cos cos sin sin
3
45
5cos 2
3 45 cos sin 25 5
4tan
3
53 8 2cos5
Q1, Q4
2cos5
66 25
53 8 66 25 ,293 35
119 33 ,346 43
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(ii) Express 3sin 3 cos3 in the form sin 3t t R t 2005 Extension 1 HSC Q5c) (i)
![Page 56: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/56.jpg)
(ii) Express 3sin 3 cos3 in the form sin 3t t R t 2005 Extension 1 HSC Q5c) (i)
3sin3 cos3t t
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(ii) Express 3sin 3 cos3 in the form sin 3t t R t 2005 Extension 1 HSC Q5c) (i)
3sin3 cos3t t sin 3 cos cos3 sint t
![Page 58: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/58.jpg)
(ii) Express 3sin 3 cos3 in the form sin 3t t R t 2005 Extension 1 HSC Q5c) (i)
3sin3 cos3t t sin 3 cos cos3 sint t
3
12
![Page 59: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/59.jpg)
(ii) Express 3sin 3 cos3 in the form sin 3t t R t 2005 Extension 1 HSC Q5c) (i)
3sin3 cos3t t sin 3 cos cos3 sint t
3
12 2sin 3t
![Page 60: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/60.jpg)
(ii) Express 3sin 3 cos3 in the form sin 3t t R t 2005 Extension 1 HSC Q5c) (i)
3sin3 cos3t t sin 3 cos cos3 sint t
3
12 2sin 3t
1tan3
30
![Page 61: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/61.jpg)
(ii) Express 3sin 3 cos3 in the form sin 3t t R t 2005 Extension 1 HSC Q5c) (i)
3sin3 cos3t t sin 3 cos cos3 sint t
3
12 2sin 3t
1tan3
30
2sin 3 30t
![Page 62: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/62.jpg)
(ii) Express 3sin 3 cos3 in the form sin 3t t R t 2005 Extension 1 HSC Q5c) (i)
3sin3 cos3t t sin 3 cos cos3 sint t
3
12 2sin 3t
1tan3
30
2sin 3 30t
(iii) Express sin cos in the form cosx x R x 2003 Extension 1 HSC Q2e) (i)
![Page 63: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/63.jpg)
(ii) Express 3sin 3 cos3 in the form sin 3t t R t 2005 Extension 1 HSC Q5c) (i)
3sin3 cos3t t sin 3 cos cos3 sint t
3
12 2sin 3t
1tan3
30
2sin 3 30t
(iii) Express sin cos in the form cosx x R x 2003 Extension 1 HSC Q2e) (i)
sin cosx x
![Page 64: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/64.jpg)
(ii) Express 3sin 3 cos3 in the form sin 3t t R t 2005 Extension 1 HSC Q5c) (i)
3sin3 cos3t t sin 3 cos cos3 sint t
3
12 2sin 3t
1tan3
30
2sin 3 30t
(iii) Express sin cos in the form cosx x R x 2003 Extension 1 HSC Q2e) (i)
sin cosx x cos cos sin sinx x
![Page 65: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/65.jpg)
(ii) Express 3sin 3 cos3 in the form sin 3t t R t 2005 Extension 1 HSC Q5c) (i)
3sin3 cos3t t sin 3 cos cos3 sint t
3
12 2sin 3t
1tan3
30
2sin 3 30t
(iii) Express sin cos in the form cosx x R x 2003 Extension 1 HSC Q2e) (i)
sin cosx x cos cos sin sinx x
cos sinx x
![Page 66: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/66.jpg)
(ii) Express 3sin 3 cos3 in the form sin 3t t R t 2005 Extension 1 HSC Q5c) (i)
3sin3 cos3t t sin 3 cos cos3 sint t
3
12 2sin 3t
1tan3
30
2sin 3 30t
(iii) Express sin cos in the form cosx x R x 2003 Extension 1 HSC Q2e) (i)
sin cosx x cos cos sin sinx x
1
12 cos sinx x
![Page 67: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/67.jpg)
(ii) Express 3sin 3 cos3 in the form sin 3t t R t 2005 Extension 1 HSC Q5c) (i)
3sin3 cos3t t sin 3 cos cos3 sint t
3
12 2sin 3t
1tan3
30
2sin 3 30t
(iii) Express sin cos in the form cosx x R x 2003 Extension 1 HSC Q2e) (i)
sin cosx x cos cos sin sinx x
1
12
2 cos x cos sinx x
![Page 68: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/68.jpg)
(ii) Express 3sin 3 cos3 in the form sin 3t t R t 2005 Extension 1 HSC Q5c) (i)
3sin3 cos3t t sin 3 cos cos3 sint t
3
12 2sin 3t
1tan3
30
2sin 3 30t
(iii) Express sin cos in the form cosx x R x 2003 Extension 1 HSC Q2e) (i)
sin cosx x cos cos sin sinx x
1
12
2 cos x
tan 145
cos sinx x
![Page 69: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/69.jpg)
(ii) Express 3sin 3 cos3 in the form sin 3t t R t 2005 Extension 1 HSC Q5c) (i)
3sin3 cos3t t sin 3 cos cos3 sint t
3
12 2sin 3t
1tan3
30
2sin 3 30t
(iii) Express sin cos in the form cosx x R x 2003 Extension 1 HSC Q2e) (i)
sin cosx x cos cos sin sinx x
1
12
2 cos x
tan 145
2 cos 45x
cos sinx x
![Page 70: 11X1 T07 07 asinx + bcosx = c (2011)](https://reader030.vdocuments.us/reader030/viewer/2022032420/55a43d6c1a28aba3378b457b/html5/thumbnails/70.jpg)
(ii) Express 3sin 3 cos3 in the form sin 3t t R t 2005 Extension 1 HSC Q5c) (i)
3sin3 cos3t t sin 3 cos cos3 sint t
3
12 2sin 3t
1tan3
30
2sin 3 30t
(iii) Express sin cos in the form cosx x R x 2003 Extension 1 HSC Q2e) (i)
sin cosx x cos cos sin sinx x
1
12
2 cos x
tan 145
2 cos 45x
cos sinx x
Exercise 2E;6, 7, 10bd, 11, 13, 14, 16ac, 20a, 23