Chapter 6: Q 101. (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 $f (2 θ)$ .

Short Answer

Expert verified

The value of the function $f (2 θ)$ is $\frac{\sqrt{3}}{2}$ .

Step by step solution

Step 1. Given information.

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

Step 2. Finding f2θ.

In trigonometric standard angel the value of $\sin 120 ° = \frac{\sqrt{3}}{2}$ .

Substitute the value in function $f (2 θ)$ .

$f (2 θ) = f (2 \times 60 °) = f (120 °)$

Further simplify.

$f (120 °) = \sin 120 ° = \sin (90 ° + 30 °) = \cos 30 ° = \frac{\sqrt{3}}{2}$

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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 $f (2 θ)$ .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Finding f2θ.

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If fθ=sinθand gθ=cosθ. Find the exact value of the function given below if θ=60°. Do not use a calculator.Function isf2θ.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Finding f2θ.

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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 $f (2 θ)$ .