Question

How do you find the general solution for `sinx = cos3x`?

Answer 1

Solve sin x = cos (3x)

Ans: `x = pi/8 + (kpi)/2`

Explanation:

Use trig identity:
`cos (3x) = sin (pi/2 - 3x)`
We get:
`sin x = sin (pi/2 - 3x)`
`x = pi/2 - 3x` -->
`4x = pi/2`+ 2kpi# --> #x = pi/8 + (kpi)/2#

Check by calculator.
`x = pi/8` --> `sin x = 22.5 = 0.38`
`3x = (3pi)/8 --> cos 3x = cos 67.5 = 0.38`. OK