Given that $x = \cos(\theta)$, we want to express $\sin(\theta)$ in terms of $x$.

We can use the Pythagorean identity:

$\sin^2(\theta) + \cos^2(\theta) = 1$

Substituting $\cos(\theta) = x$ into the identity:

$\sin^2(\theta) + x^2 = 1$

Now, solve for $\sin^2(\theta)$:

$\sin^2(\theta) = 1 - x^2$

Taking the square root of both sides:

$\sin(\theta) = \pm \sqrt{1 - x^2}$

Therefore, $\sin(\theta)$ in terms of $x$ is:

$\sin(\theta) = \pm \sqrt{1 - x^2}$

The $\pm$ sign depends on the quadrant in which the angle $\theta$ is located.

Would you like further details or have any questions?

Here are 5 related questions you might consider:

1. What is $\tan(\theta)$ in terms of $x$?
2. How do you determine the correct sign for $\sin(\theta)$?
3. What is $\sin(2\theta)$ in terms of $x$?
4. Can you express $\theta$ in terms of $x$?
5. How would you solve for $\theta$ given a specific value of $x$?

Tip: Remember that the sign of $\sin(\theta)$ depends on the angle's quadrant in the unit circle.