Given that sin(x)=78, what is sin(−x)?

The sine function has the property that it is **odd**, meaning that:

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

Given that \(\sin(x) = 78\), we can now find \(\sin(-x)\) by applying this property:

\[
\sin(-x) = -\sin(x) = -78
\]

So, \(\sin(-x) = -78\).

Do you need further clarification on this concept? Here are 5 related questions to expand your understanding:

1. What is the general formula for other trigonometric functions when given negative angles?
2. Why are sine and tangent functions classified as odd, but cosine as even?
3. How would \(\cos(-x)\) compare to \(\cos(x)\)?
4. What are the implications of this property on the unit circle?
5. Can you explain the symmetry of the sine function in relation to the origin?

**Tip:** In trigonometry, remembering whether functions are odd or even helps solve many problems with negative angles.

Learn how to use the odd property of the sine function to find sin(-x) when sin(x) = 78. This problem explores key trigonometric concepts such as odd and even functions and their application in solving negative angle problems. Suitable for students in Grades 10-12.

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