Question

use identities to fill in the blank
if \\( \sin \theta = \frac { 2 } { 7 } \\), then \\( - \sin ( - \theta ) = \\)
\\( - \sin ( - \theta ) = \\) (type an integer or a fraction.)

Explanation:

Step1: Use the odd - function identity for sine

The sine function is an odd function, which means \(\sin(-\theta)=-\sin\theta\).

Step2: Substitute the given value of \(\sin\theta\)

We are given that \(\sin\theta = \frac{2}{7}\).
Now, \(-\sin(-\theta)=-(-\sin\theta)\) (since \(\sin(-\theta)=-\sin\theta\)).
Simplifying \(-(-\sin\theta)\) gives \(\sin\theta\).
Substituting \(\sin\theta=\frac{2}{7}\), we get \(-\sin(-\theta)=\frac{2}{7}\).

Answer:

\(\frac{2}{7}\)