Chapter 6: Q 114. (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 $(h \cdot f) (\frac{5 π}{6})$ .

Short Answer

Expert verified

The value of $(h \cdot f) (\frac{5 π}{6})$ is $\frac{5 π}{6}$ .

Step by step solution

Step 1. Given information.

Given $h (x) = 2 x$ role="math" localid="1646553814626" $, f (x) = \sin x$ and the value of $x$ is $\frac{5 π}{6}$ .

Step 2. Simplify the given expression.

$(h \cdot f) (\frac{5 π}{6})$ can be written as $h (\frac{5 π}{6})$ and $f (\frac{5 π}{6})$ .

Substitute $2 x$ for $h (\frac{5 π}{6})$ and $\sin x$ for $f (\frac{5 π}{6})$ .

$(h \cdot f) (\frac{5 π}{6}) = (2 \times \frac{5 π}{6} \cdot \sin \frac{5 π}{6})$

Step 3. Find the valuer of h·f 5π6.

In trigonometric standard angle the value of $\sin \frac{5 π}{6}$ is $\frac{1}{2}$ .

Substitute the value in the simplified expression.

$(h \cdot f) (\frac{5 π}{6}) = (2 \times \frac{5 π}{6} \cdot \sin \frac{5 π}{6}) = (\frac{5 π}{3} \cdot \frac{1}{2}) = \frac{5 π}{6}$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

If $f (x) = \sin x, g (x) = \cos x$ and $h (x) = 2 x, P (x) = \frac{x}{2}$ .Find the value of $(h \cdot f) (\frac{5 π}{6})$ .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the given expression.

Step 3. Find the valuer of h·f 5π6.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Geometry

Discrete Mathematics

Calculus

Statistics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Iffx=sinx,gx=cosxandhx=2x,Px=x2.Find the value ofh·f5π6.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the given expression.

Step 3. Find the valuer of h·f 5π6.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Geometry

Discrete Mathematics

Calculus

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 $(h \cdot f) (\frac{5 π}{6})$ .