Write h in simplest form h(x)=2 * cos(x-90)+2

To simplify the function \( h(x) = 2 \cdot \cos(x - 90^\circ) + 2 \), we can use the trigonometric identity:

\[
\cos(x - 90^\circ) = -\sin(x)
\]

Therefore, the function becomes:

\[
h(x) = 2 \cdot (-\sin(x)) + 2
\]

Simplifying further:

\[
h(x) = -2\sin(x) + 2
\]

Thus, the simplest form of \( h(x) \) is:

\[
\boxed{h(x) = -2\sin(x) + 2}
\]

Would you like more details, or do you have any questions about this process?

Here are 5 related questions you might explore:
1. How does the phase shift in trigonometric functions affect the graph of the function?
2. What is the amplitude of the function \( h(x) = -2\sin(x) + 2 \)?
3. How do you determine the maximum and minimum values of \( h(x) = -2\sin(x) + 2 \)?
4. What are the key differences between the graphs of sine and cosine functions?
5. How would \( h(x) \) change if we added a horizontal shift?

**Tip:** Understanding trigonometric identities, like the one used here, is essential for simplifying and transforming trigonometric functions.

Learn how to simplify the trigonometric function h(x) = 2 * cos(x-90)+2 step-by-step. Understand the application of trigonometric identities, specifically the identity \( \cos(x - 90^\circ) = -\sin(x) \). Suitable for Grades 10-12 students studying trigonometry.

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