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

sin (2θ) = 24/25

Step-by-step 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}}=(3)/(5)`

And,

`\cos \theta=\frac{\text{adjacent}}{\text{hypotenuse}}=(4)/(5)`

Replace into the expanded expression,

`\sin 2\theta=2\cdot(3)/(5)\cdot(4)/(5)`

And solve,

`\sin 2\theta=(2\cdot3\cdot4)/(5\cdot5)=(24)/(25)`

Hence, sin(2θ) = 24/25