Question

How do you find the general solutions for `sqrt3 sinx - cosx = 1`?

Answer 1

Solve `sqrt3sin x - cos x = 1`

Ans: 13.22 and 133.22 deg

Explanation:

Divide both side by sqrt3.
`sin x - 1/sqrt3.cos x = 1/sqrt3`
Replace in the left side, `1/sqrt3 = tan 60 = sin 60/cos 60`
`sin x.cos 60 - sin 60.cos x = (1/sqrt3)(cos 60) = 1/(2sqrt3)`
`sin (x - 60) = 1/(2sqrt3) = 0.29`
Calculator gives:
`(x - 60) = +- 73.22`

a. x - 60 = 73.22 --> x = 60 + 73.22 = 133.22 deg
b. x - 60 = - 73.22 --> x = -73.22 + 60 = 13.22 deg