I'm new to Trig and don't understand.....

Question

I do not understand how to solve this question. I have searched many websites and have not found any information on how to do it.

Find the values for $\theta$ that make each statement true

$$\sin(\theta)=\cos(25^{\circ})$$

Answer 1

You'll need to use a trigonometric identity.

In the first quadrant, there is the identity

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

Treat $\theta$ like a variable, and solve.

Answer 2

Hint: For $\space x=90°- \alpha, \space$ we have:

$$\cos \alpha = \sin x = \sin (90°- \alpha).$$

Answer 3

$sin(\theta)=cos(\frac{\pi}{2}-\theta)$ and thus we have that

$cos(\frac{\pi}{2}-\theta)=cos(25) \\ \Rightarrow \frac{\pi}{2}-\theta=2n\pi\pm 25$

(you can check that these are the only solutions of the equation)

Answer 4

Hint:

Since $$\cos (x) = \sin (90°-x)$$ $$\cos 25° = \ ?$$