Chapter 7: Q. 30 (page 495)

In Problems 29– 40, use the figures to evaluate each function given that
$f (x) = \sin x g (x) = \cos x h (x) = \tan x$
$g (2 θ)$

Short Answer

Expert verified

The evaluation of $g (2 θ)$ is $- \frac{3}{5}$

Step by step solution

Step 1. Given

The figures:

The function $f (x) = \sin x g (x) = \cos x h (x) = \tan x$

To evaluate the value of $g (2 θ)$

Step 2. Find the equation.

$g (x) = \cos x g (2 θ) = \cos 2 θ$

From the figure, the equation of circle is

$x^{2} + y^{2} = 5$

Step 3. Find sin θ

From the right triangle,

$\sin θ = \frac{2}{\sqrt{5}}$

Step 4. Use double-angle formula

By using double-angle formula,

$\cos 2 θ = 1 - 2 \sin^{2} θ = 1 - 2 {(\frac{2}{\sqrt{5}})}^{2} = 1 - 2 (\frac{4}{5}) = 1 - \frac{8}{5} = - \frac{3}{5}$

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In Problems 29– 40, use the figures to evaluate each function given that
$f (x) = \sin x g (x) = \cos x h (x) = \tan x$
$g (2 θ)$

Short Answer

Step by step solution

Step 1. Given

Step 2. Find the equation.

Step 3. Find sin θ

Step 4. Use double-angle formula

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In Problems 29– 40, use the figures to evaluate each function given thatf(x)=sinxg(x)=cosxh(x)=tanxg(2θ)

Short Answer

Step by step solution

Step 1. Given

Step 2. Find the equation.

Step 3. Find sin θ

Step 4. Use double-angle formula

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Geometry

Pure Maths

Theoretical and Mathematical Physics

Logic and Functions

Statistics

Study anywhere. Anytime. Across all devices.

In Problems 29– 40, use the figures to evaluate each function given that
$f (x) = \sin x g (x) = \cos x h (x) = \tan x$
$g (2 θ)$