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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.

Use the triangle to find the exact value of the trigonometric function. No decimal-example-1

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ANSWER

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

User Sheena Singla
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