Chapter 6: Q 112. (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 $(g \cdot p) (60 °)$ .

Short Answer

Expert verified

The value of function $(g \cdot p) (60 °)$ is $\frac{\sqrt{3}}{4}$ .

Step by step solution

Step 1. Given information.

Given $f (x) = \sin x, g (x) = \cos x$ and the value of $x$ is $60 °$ .

Step 2. Simplify the given expression.

$(g \cdot p) (60 °)$ can be written as $g (60 °)$ and $p (60 °)$ .

Substitute $\cos 60 °$ for $g (60 °)$ and $\sin 60 °$ for $f (60 °)$ .

$(g \cdot p) (60 °) = (\cos 60 ° \cdot \sin 60 °)$

Step 3. Find the value of g·p 60°.

In trigonometric standard angle the value of $\cos 60 ° = \frac{1}{2}$ and the value of $\sin 60 ° = \frac{\sqrt{3}}{2}$ .

Substitute the values of angles in simplified expression.

$(g \cdot p) (60 °) = (\cos 60 ° \cdot \sin 60 °) = (\frac{1}{2} \cdot \frac{\sqrt{3}}{2}) = \frac{\sqrt{3}}{4}$

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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 $(g \cdot p) (60 °)$ .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the given expression.

Step 3. Find the value of g·p 60°.

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Iffx=sinx,gx=cosxandhx=2x,Px=x2.Find the value ofg·p60°.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the given expression.

Step 3. Find the value of g·p 60°.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Pure Maths

Discrete Mathematics

Probability and Statistics

Statistics

Theoretical and Mathematical Physics

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 $(g \cdot p) (60 °)$ .