Chapter 6: Q 113. (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 the function $(p \cdot g) (315 °)$ .

Short Answer

Expert verified

The value of the function $(p \cdot g) (315 °)$ is $- \frac{1}{2}$ .

Step by step solution

Step 1. Given information.

Given $f (x) = \sin x, g (x) = \cos x$ and $h (x) = 2 x, P (x) = \frac{x}{2}$ and the value of $x$ is $315 °$ .

Step 2. Simplify the given expression.

$(p \cdot g) (315 °)$ can be written as $p (315 °)$ and $g (315 °)$ .

Substitute $\sin 315 °$ for $p (315 °)$ and $\cos 315 °$ for $g (315 °)$ .

$(p \cdot g) (315 °) = (\sin 315 ° \cdot \cos 315 °)$

Step 3. Find the value of p·g 315°.

In trigonometric standard angle the value of $\sin 315 °$ is $- \frac{1}{\sqrt{2}}$ and the value of $\cos 315 °$ is $\frac{1}{\sqrt{2}}$ .

Substitute the value of angles in the simplified expression.

$(p \cdot g) (315 °) = (\sin 315 ° \cdot \cos 315 °) = (- \frac{1}{\sqrt{2}} \cdot \frac{1}{\sqrt{2}}) = - \frac{1}{2}$

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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 the function $(p \cdot g) (315 °)$ .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the given expression.

Step 3. Find the value of p·g 315°.

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Iffx=sinx,gx=cosxandhx=2x,Px=x2.Find the value of the functionp·g315°.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the given expression.

Step 3. Find the value of p·g 315°.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Mechanics Maths

Applied Mathematics

Geometry

Theoretical and Mathematical Physics

Decision Maths

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 the function $(p \cdot g) (315 °)$ .