Question

Use the triangle to find the exact value of the trigonometric function. No decimal answers. Show all work.Hint: Use an identity to expand the expression.

Answer 1

ANSWER

sin (2θ) = 24/25

EXPLANATION

As shown in the hint we can use an identity to expand sin(2θ),

$\sin 2\theta=2\sin \theta\cos \theta$

From the triangle, we know,

$\sin \theta=\frac{\text{opposite}}{\text{hypotenuse}}=\frac{3}{5}$

And,

$\cos \theta=\frac{\text{adjacent}}{\text{hypotenuse}}=\frac{4}{5}$

Replace into the expanded expression,

$\sin 2\theta=2\cdot\frac{3}{5}\cdot\frac{4}{5}$

And solve,

$\sin 2\theta=\frac{2\cdot3\cdot4}{5\cdot5}=\frac{24}{25}$

Hence, sin(2θ) = 24/25