Question

Find the value for θ.

sinθ=cos(θ−18.5)

Answer 1

`\theta=54.25` in the interval
`0\leq\theta\leq90`°

Explanation:

I assume the angles are in degrees and the interval is from 0 to 90 degrees.

Given:

`\sin \theta=\cos(\theta-18.5)`

We know that,

`\sin \theta=\cos(90-\theta)`

Therefore, replace
`\sin \theta` by
`\cos(90-\theta)`, we get:

`\cos(90-\theta)=\cos(\theta-18.5)`

`90-\theta=\theta-18.5\\90+18.5=\theta+\theta\\108.5=2\theta\\\theta=(108.5)/(2)=54.25`

Therefore, the value of
`\theta=54.25`