Question

Find the value for θ. sinθ=cos(θ−18.5)

Answer 1

Answer:

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

Step-by-step 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:

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

$90-\theta=\theta-18.5\\90+18.5=\theta+\theta\\108.5=2\theta\\\theta=\frac{108.5}{2}=54.25$

Therefore, the value of $\theta=54.25$