Understanding Engineering Mathematics

(やまだぃちぅ) #1

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
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