Chapter 6: Q 98. (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 calculator.
Function is $g (\frac{θ}{2})$ .

Short Answer

Expert verified

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

Step by step solution

Step 1. Given information.

Consider the given function $g (\frac{θ}{2})$ and the value of $θ = 60 °$ .

Step 2. Finding gθ2.

In the trigonometric standard angles the value of $\cos 30 ° = \frac{\sqrt{3}}{2}$ .

Substitute the value in $g (\frac{θ}{2})$ .

$g (\frac{θ}{2}) = g (\frac{60 °}{2}) g (\frac{θ}{2}) = g (30 °)$

Further simplify.

$g (30 °) = \cos 30 ° = \frac{\sqrt{3}}{2}$

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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 calculator.
Function is $g (\frac{θ}{2})$ .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Finding gθ2.

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Short Answer

Step by step solution

Step 1. Given information.

Step 2. Finding gθ2.

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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 calculator.
Function is $g (\frac{θ}{2})$ .