Answer:
[tex]\theta=54.25[/tex] in the interval [tex]0\leq\theta\leq90[/tex]°
Step-by-step explanation:
I assume the angles are in degrees and the interval is from 0 to 90 degrees.
Given:
[tex]\sin \theta=\cos(\theta-18.5)[/tex]
We know that,
[tex]\sin \theta=\cos(90-\theta)[/tex]
Therefore, replace [tex]\sin \theta[/tex] by [tex]\cos(90-\theta)[/tex], we get:
[tex]\cos(90-\theta)=\cos(\theta-18.5)[/tex]
[tex]90-\theta=\theta-18.5\\90+18.5=\theta+\theta\\108.5=2\theta\\\theta=\frac{108.5}{2}=54.25[/tex]
Therefore, the value of [tex]\theta=54.25[/tex]
