Chapter 6: Q 111. (page 382)

If $f (x) = \sin x, g (x) = \cos x$ and $h (x) = 2 x, P (x) = \frac{x}{2}$ .Find the value of $(f \cdot h) (\frac{π}{6})$ .

Short Answer

Expert verified

The value of $(f \cdot g) (\frac{π}{6})$ is $\frac{\sqrt{3}}{4}$ .

Step by step solution

Step 1. Given information.

Given $f (x) = \sin x, g (x) = \cos x$ and $h = 2 x, P (x) = \frac{x}{2}$ and the value of $x$ is $\frac{π}{6}$ .

Step 2. Simplify the given expression.

$(f \cdot g) (\frac{π}{6})$ can be written as $f (\frac{π}{6})$ and $g (\frac{π}{6})$ .

Substitute $\sin (\frac{π}{6})$ for $f (\frac{π}{6})$ and $\cos (\frac{π}{6})$ for $g (\frac{π}{6})$ .

then,

$(f \cdot g) (\frac{π}{6}) = (\sin \frac{π}{6} \cdot \cos \frac{π}{6})$

Step 3. Find the value of f·g π6.

In trigonometric standard angle the value of $\sin (\frac{π}{6})$ is $\frac{1}{2}$ and the value of $\cos (\frac{π}{6})$ is $\frac{\sqrt{3}}{2}$ .

Substitute the values in simplified expression.

$(f \cdot g) (\frac{π}{6}) = (\sin \frac{π}{6} \cdot \cos \frac{π}{6}) = (\frac{1}{2} \cdot \frac{\sqrt{3}}{2}) = (\frac{\sqrt{3}}{4})$

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If $f (x) = \sin x, g (x) = \cos x$ and $h (x) = 2 x, P (x) = \frac{x}{2}$ .Find the value of $(f \cdot h) (\frac{π}{6})$ .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the given expression.

Step 3. Find the value of f·g π6.

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Iffx=sinx,gx=cosxandhx=2x,Px=x2.Find the value off·hπ6.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the given expression.

Step 3. Find the value of f·g π6.

One App. One Place for Learning.

Most popular questions from this chapter

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Probability and Statistics

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Study anywhere. Anytime. Across all devices.

If $f (x) = \sin x, g (x) = \cos x$ and $h (x) = 2 x, P (x) = \frac{x}{2}$ .Find the value of $(f \cdot h) (\frac{π}{6})$ .