Question

Hi! I was absent in class and did not understand this lesson please I will be really grateful if you help me ! I appreciate it this is classwork assignment does not count as a test

Answer 1

ANSWER

$\frac{240}{289}$

EXPLANATION

We want to find the value of the expression using the given figure:

$\sin (2\theta)$

To do this, let us rewrite the expression in terms of its trigonometric identity:

$\sin (2\theta)=2\sin \theta\cos \theta$

To solve this we can apply trigonometric ratios SOHCAHTOA for right triangles to find the values of sine and cosine:

$\begin{gathered} \sin \theta=\frac{\text{opposite}}{\text{hypotenuse}} \\ \cos \theta=\frac{\text{adjacent}}{\text{hypotenuse}} \end{gathered}$

For the given triangle, we have that:

$\begin{gathered} \sin \theta=\frac{8}{17} \\ \cos \theta=\frac{15}{17} \end{gathered}$

Therefore, the value of the expression is:

$\begin{gathered} \sin 2\theta=2\cdot\frac{8}{17}\cdot\frac{15}{17} \\ \sin 2\theta=\frac{240}{289} \end{gathered}$

That is the answer.