Question

Question #a3292

Answer 1

Solve 3cos x - 4sin x = 2

Explanation:

Divide both sides by 3
`cos x - (4/3)sin x = 2/3`
Call `tan a = (sin a)/(cos a) = 4/3` -> `a = 53^@13`, we get:
`cos x - (sina)/(cos a)sin x = 2/3`
`cos x.cos a - sin a.sin x = (2cos a)/3 = (2(0.60))/3 = 0.40`
cos (x + a) = (x + 53.13) = 0.40

`(x + 53.13) = +- 66^@42`

a. x + 53.13 = 66.42 --> `x = 13.29`
b. x + 53.13 = -66.42 --> `x = -66.42 - 53.13 = - 119.55 (or 240.45)`
General solutions:
x = 13.29 + k360
x = 240.45 + k360