EXAMPLE 13

Solve : 3 sin x + 4 cos x = 2

Solution : 3 sin x + 4 cos x = 2 \ a = 3, b = 4 and c = 2

Dividing by 5 to the given equation

i.e. 0.6 sin x + 0.8 cos x = 0.4

\ sin 36⁰ 52' sin x + cos 36⁰ 52' cos x = cos 66⁰ 25'

i.e. cos (x - 36⁰0 52') = cos 66⁰ 25'

The general solution is x - 36⁰ 52' = n (3600) ± 66.25'

i.e. x = n (360⁰) + 1030 17' or n (360⁰) - 29⁰ 33'

EXAMPLE 14

Solve cos 2x = 3 (sin x - 1) for all values of x

Solution : cos 2x = 3(sin x -1)

1 - 2 sin 2x = 3 sin x -3 ..........( since cos 2x = 1 - 2 sin 2x)

2 sin 2x + 3 sin x - 4 = 0

Comparing with ax² + bx + c = 0 form,

a = 2, b = 3 and c = - 4

Then using

since then -2.351 is impossible.

Taking sin x =0.8508x =1.0175 in radians.

x = 58.3⁰ + 2nin degrees.

x = 58.3⁰ + n(360⁰)

and x = 2.124 + 2nor x = 121.7 ⁰ + n (360⁰)

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Index

6.1 Inverse Functions
6.2 Trignometric Equations
Supplementary Problems

Chapter 7