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

`(240)/(289)`

Step-by-step 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=(8)/(17) \\ \cos \theta=(15)/(17) \end{gathered}`

Therefore, the value of the expression is:

`\begin{gathered} \sin 2\theta=2\cdot(8)/(17)\cdot(15)/(17) \\ \sin 2\theta=(240)/(289) \end{gathered}`

That is the answer.