The task in the image is asking to write a sine function equivalent to $f(x) = \cos(x)$.

To find an equivalent sine function for $\cos(x)$, we can use the phase shift property of trigonometric functions.

We know from trigonometry that: $\cos(x) = \sin\left(x + \frac{\pi}{2}\right)$ This is because the sine function is shifted $\frac{\pi}{2}$ (or 90°) to the left compared to the cosine function.

Therefore, the sine function equivalent to $f(x) = \cos(x)$ is: $f(x) = \sin\left(x + \frac{\pi}{2}\right)$

Would you like further details or explanations on how this phase shift works?

Here are 5 related questions to further explore this topic:

1. What are the properties of sine and cosine functions?
2. How do phase shifts affect the graphs of trigonometric functions?
3. Can you convert any sine function into a cosine function?
4. What is the general form of a sine or cosine function with phase shift and amplitude?
5. How does the period of sine and cosine functions relate to their equations?

Tip: Trigonometric identities, like the one used here, are essential in simplifying expressions and solving equations in calculus and physics!