Question

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

Answer 1

Answer:

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:

$\begin{gathered} \sin \theta=\frac{\text{Opposite}}{\text{Hypotenuse}}=\frac{3}{5} \\ \cos \theta=\frac{\text{Adjacent}}{\text{Hypotenuse}}=\frac{4}{5} \end{gathered}$

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

$\begin{gathered} \sin 2\theta=2\sin \theta\cos \theta \\ =2\times\frac{3}{5}\times\frac{4}{5} \\ =\frac{24}{25} \end{gathered}$

The exact value of sin(2θ) is 24/25.