Chapter 6: Q 99. (page 381)

If $f (θ) = \sin θ$ and $g (θ) = \cos θ$ . Find the exact value of the function given below if $θ = 60 °$ . Do not use a calculator.
Function is ${[f (θ)]}^{2}$ .

Short Answer

Expert verified

The value of the function ${[f (θ)]}^{2}$ is $\frac{3}{4}$ .

Step by step solution

Step 1. Given information.

Consider the given function $f (θ) = \sin θ$ and the value of $θ = 60 °$ .

Step 2. Finding fθ2.

In the trigonometric standard angle the value of $\sin 60 ° = \frac{\sqrt{3}}{2}$ .

Substitute the value in function ${[f (θ)]}^{2}$ .

${[f (θ)]}^{2} = {[\sin 60 °]}^{2} = {[\frac{\sqrt{3}}{2}]}^{2} = \frac{3}{4}$

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If $f (θ) = \sin θ$ and $g (θ) = \cos θ$ . Find the exact value of the function given below if $θ = 60 °$ . Do not use a calculator.
Function is ${[f (θ)]}^{2}$ .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Finding fθ2.

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Step by step solution

Step 1. Given information.

Step 2. Finding fθ2.

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If $f (θ) = \sin θ$ and $g (θ) = \cos θ$ . Find the exact value of the function given below if $θ = 60 °$ . Do not use a calculator.
Function is ${[f (θ)]}^{2}$ .