Understanding Engineering Mathematics

D. (i)^12 (sin 5x−sinx) (ii)^12 (cos 3x−cos 5x) (iii)^12 (sin 3x−sinx)

(iv)^12 (cos 9x+cosx)

6.3.8 Trigonometric equations

A. (i) 2nπ±

π

2

(ii) Undefined, or ‘∞’ (iii) 2nπ±

5 π

6

(iv) nπ

(v) nπ+(− 1 )n

π

2

(vi) No solutions (vii) nπ (viii) nπ+

3 π

4

B. (i) nπ (ii) 2nπor

( 2 n+ 1 )

3

π (iii)

2

3

nπ+

π

2

(iv)

( 2 n+ 1 )

5

π (v) nπ+

π

4

(vi) nπ+ 1. 11

6.3.9 TheacosqYbsinqform

A. (i) (a)

√

2sin

(

θ−

π

4

)

(b)

√

2cos

(

θ−

3 π

4

)

(ii) (a) 2 sin

(

θ+

π

3

)

(b) 2 cos

(

θ−

π

6

)

(iii) (a) 2 sin

(

θ−

π

6

)

(b) 2 cos

(

θ−

5 π

6

)

(iv) (a) 5 sin(θ+ 36. 9 °) (b) 5 cos(θ− 53. 1 °)

B. (i) Max of

√

2at

3 π

4

Min of−

√

2at

7 π

4

(ii) Max of 2 at

π

6

Min of−2at

7 π

6

(iii) Max of 2 at

2 π

3

Min of−2at

5 π

3

(iv) Max of 5 at 2.21 rads Min of−5at5.35rads

C. (i) (a)

π

2

,

3 π

2

(b) 0,π

(ii) (a)

π

2

,

5 π

3

(b)

5 π

6

,

3 π

2

(iii) (a)

π

3

,π (b)

4 π

3

,2π

(iv) (a) 2.3 rads, 5.84 rads (b) 2.7 rads, 5.44 rads