Question

Find the value for θ.

sinθ=cos(θ−18.5)
Question 6 options:

35.75°


71.5°


54.25°


161.5°

Answer 1

`\theta=54.25\°`

Explanation:

we know that

When the sine of angle X is equal to the cosine of angle Y, then angle X and angle Y are complementary angles

so

`X+Y=90\°`----> equation A

In this problem

`X=\theta`

`Y=(\theta-18.5)`

substitute in the equation A

`\theta\°+(\theta-18.5)\°=90\°`

`2\theta=90+18.5`

`2\theta=108.5`

`\theta=54.25\°`