# 11x1 t08 07 asinx + bcosx = c (2010)

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• Equations of the form asinx + bcosx = cMethod 1: Using the t results

• Equations of the form asinx + bcosx = cMethod 1: Using the t results

3600 eg (i) 3cos 4sin 2

• Equations of the form asinx + bcosx = cMethod 1: Using the t results

3600 eg (i) 3cos 4sin 2 let tan

2t

• 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

• 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

• 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

• 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

• 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 tan

2 5 2 5

• 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 tan

2 5 2 5

Q2

• 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 tan

2 5 2 5

Q2 21 4tan5

6 39

• 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 tan

2 5 2 5

Q2 21 4tan5

6 39

173 212

346 42

• 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 tan

2 5 2 5

Q2 21 4tan5

6 39

173 212

346 42

Q1

• 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 tan

2 5 2 5

Q2 21 4tan5

6 39

173 212

346 42

Q1 4 21tan5

59 47

• 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 tan

2 5 2 5

Q2 21 4tan5

6 39

173 212

346 42

Q1 4 21tan5

59 47

59 472

119 33

• 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 tan

2 5 2 5

Q2 21 4tan5

6 39

173 212

346 42

Q1 4 21tan5

59 47

59 472

119 33

180: Test

• 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 tan

2 5 2 5

Q2 21 4tan5

6 39

173 212

346 42

Q1 4 21tan5

59 47

59 472

119 33

180: Test3cos180 4sin180

4 2

• 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 tan

2 5 2 5

Q2 21 4tan5

6 39

173 212

346 42

Q1 4 21tan5

59 47

59 472

119 33

180: Test3cos180 4sin180

4 2

119 33 ,346 42

• Method 2: Auxiliary Angle Method(i) Change into a sine functioneg (i) 3cos 4sin 2 3600

• Method 2: Auxiliary Angle Method(i) Change into a sine functioneg (i) 3cos 4sin 2 3600

3cos 4sin 2

• Method 2: Auxiliary Angle Method(i) Change into a sine functioneg (i) 3cos 4sin 2 3600

3cos 4sin 2 sincoscossin

• Method 2: Auxiliary Angle Method(i) Change into a sine functioneg (i) 3cos 4sin 2 3600

3cos 4sin 2 sincoscossin

• 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

• Method 2: Auxiliary Angle Method(i) Change into a sine functioneg (i) 3cos 4sin 2 3600

3cos 4sin 2 sincoscossin

3

• 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

• 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

• 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

• 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

• 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

• 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

3tan4

2sin

5

• 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

3tan4

36 52 2sin

5

• 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

3tan4

36 52 2sin

5 Q1, Q2

• 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

3tan4

36 52 2sin

5 Q1, Q2

2sin5

• 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

3tan4

36 52 2sin

5 Q1, Q2

2sin5

23 35

• 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

3tan4

36 52 2sin

5 Q1, Q2

2sin5

23 35

36 52 23 35 ,156 25

• 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

3tan4

36 52 2sin

5 Q1, Q2

2sin5

23 35

36 52 23 35 ,156 25 13 17 ,119 33

• 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

3tan4

36 52 2sin

5 Q1, Q2

2sin5

23 35

36 52 23 35 ,156 25 119 33 ,346 43 13 17 ,119 33

• Method 2: Auxiliary Angle Method(ii) Change into a cosine functioneg (i) 3cos 4sin 2 3600

• Method 2: Auxiliary Angle Method(ii) Change into a cosine functioneg (i) 3cos 4sin 2 3600

3cos 4sin 2

• Method 2: Auxiliary Angle Method(ii) Change into a cosine functioneg (i) 3cos 4sin 2 3600

3cos 4sin 2 cos cos sin sin

• Method 2: Auxiliary Angle Method(ii) Change into a cosine functioneg (i) 3cos