If $x=4\cos\theta$, then find $\sinθ$ in terms of $x$.

Question

I know you shouldn't ask questions like this, but I do not know how to even start this problem.

Suppose $x=4\cos\theta$. Find $\sin\theta$ in terms of $x$.

Answer 1

HINT: Square both sides so that$$x^2=16\cos^2\theta$$and recall that$$\cos^2\theta=1-\sin^2\theta$$Thus$$x^2=16\left(1-\sin^2\theta\right)$$

Answer 2

Scratching our heads to find a relation between the sine and the cosine, we recall that

$$\cos^2\theta+\sin^2\theta=1.$$

In other words,

$$\sin^2\theta=1-\frac{x^2}{4^2}.$$