https://file.aiquickdraw.com/mathbot/file/1727495653484yntk68ez.jpg

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!

Write a sine function that is equivalent to f(x) = cos(x).

Discover how to express cos(x) as an equivalent sine function by applying the phase shift property. Learn how cos(x) can be rewritten as sin(x + π/2), making use of key trigonometric identities. Suitable for high school students in Grades 9-12.

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