Chapter 6: Q 97. (page 381)

If $f (θ) = \sin θ$ and $g (θ) = \cos θ$ . Find the value of the function given below. Do not use calculator.
Function is $f (\frac{θ}{2})$ .

Short Answer

Expert verified

The value of $f (\frac{θ}{2})$ is $\frac{1}{2}$ .

Step by step solution

Step 1. Given information.

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

Step 2. Finding fθ2.

In trigonometric standard angles the value of $\sin 30 ° = \frac{1}{2}$ .

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

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

Further simplify.

$f (θ) = \sin θ f (30 °) = \sin 30 ° f (30 °) = \frac{1}{2}$

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If $f (θ) = \sin θ$ and $g (θ) = \cos θ$ . Find the value of the function given below. Do not use calculator.
Function is $f (\frac{θ}{2})$ .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Finding fθ2.

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Short Answer

Step by step solution

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Step 2. Finding fθ2.

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If $f (θ) = \sin θ$ and $g (θ) = \cos θ$ . Find the value of the function given below. Do not use calculator.
Function is $f (\frac{θ}{2})$ .