Question

How can I use the figure to find the exact value of sin 2theta?

Answer 1

sin(2θ) = 24/25

Explanation:

In order to find the value of sin 2θ, first, recall the double-angle formula for sine.

`\sin 2\theta=2\sin \theta\cos \theta`

From the right-triangle:

`\begin{gathered} \sin \theta=\frac{\text{Opposite}}{\text{Hypotenuse}}=(3)/(5) \\ \cos \theta=\frac{\text{Adjacent}}{\text{Hypotenuse}}=(4)/(5) \end{gathered}`

Substitute these values into the double-angle formula obtained earlier.

`\begin{gathered} \sin 2\theta=2\sin \theta\cos \theta \\ =2*(3)/(5)*(4)/(5) \\ =(24)/(25) \end{gathered}`

The exact value of sin(2θ) is 24/25.