Mathematics

The key is recognizing that $\cos\left(\theta-\dfrac{\pi}{2}\right)$ can be simplified using a cofunction identity rather than finding $\theta$ explicitly. Since $\cos(A - B) = \cos A \cos B + \sin A \sin B$, or more directly, recall that $\cos\left(x - \dfrac{\pi}{2}\right) = \sin x$. Once you apply this identity, your answer depends only on the given value of $\sin\theta$, not on which specific angle $\theta$ is.

The key is recognizing that $\cos\left(\theta-\dfrac{\pi}{2}\right)$ can be simplified using a cofunction identity rather than finding $\theta$ explicitly. Since $\cos(A - B) = \cos A \cos B + \sin A \sin B$, or more directly, recall that $\cos\left(x - \dfrac{\pi}{2}\right) = \sin x$. Once you apply this identity, your answer depends only on the given value of $\sin\theta$, not on which specific angle $\theta$ is.