The equation \( y = \sin(-x^\circ) \) represents the sine function with a reflection across the \( y \)-axis. In trigonometry, the sine function has an odd symmetry, meaning:

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

So, the equation \( y = \sin(-x^\circ) \) simplifies to:

\[
y = -\sin(x^\circ)
\]

### Key Points:
1. The graph of \( y = \sin(-x^\circ) \) is a reflection of the graph of \( y = \sin(x^\circ) \) about the \( x \)-axis.
2. The amplitude (height of peaks and troughs) remains unchanged, which is 1.
3. The period remains \( 360^\circ \), as sine's period does not depend on sign.
4. The phase shift is zero since no horizontal translation is present.

### Visualization
If graphed, \( y = \sin(-x^\circ) \) would look like the sine wave flipped vertically compared to \( y = \sin(x^\circ) \).

Would you like a graph to illustrate this?

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### Further Exploration:
1. What is the relationship between \( \sin(x^\circ) \) and other trigonometric functions when \( x \) is negative?
2. How does the transformation \( \sin(-x^\circ) \) differ from \( \cos(-x^\circ) \)?
3. What happens to the period and amplitude if you multiply \( \sin(-x^\circ) \) by a constant?
4. How does \( \sin(-x^\circ) \) behave for values of \( x \) greater than \( 360^\circ \)?
5. What are the differences in phase shifts and transformations between sine and cosine?

**Tip:** Remember that odd and even properties of trigonometric functions are useful for simplifying equations!

Explore the properties of the sine function Y = sin(-x°). Learn about odd functions, the formula sin(-x) = -sin(x), and how this transformation affects the graph, amplitude, and period of the sine wave. Suitable for high school students in Grades 9-12.

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