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Q. 43PA

Expert-verified
Found in: Page 768

### Algebra 2

Book edition Middle English Edition
Author(s) Carter
Pages 804 pages
ISBN 9780079039903

# What is the period of $f\left(x\right)=\frac{1}{2}\mathrm{cos}\left(3x\right)$ and then graph the function.$\left(A\right)120{}^{\circ }\left(B\right)180{}^{\circ }\left(C\right)360{}^{\circ }\left(D\right)720°$

The period of $f\left(x\right)=\frac{1}{2}\mathrm{cos}\left(3x\right)$ is $120°$. So, option (A) is correct.

See the step by step solution

## Step 1. Write down the given information.

The given function is $f\left(x\right)=\frac{1}{2}\mathrm{cos}\left(3x\right)$.

## Step 2. Concept used.

A function of the form $y=a\mathrm{sin}\left(bx\right)\text{and}y=a\mathrm{cos}\left(bx\right)$ has amplitude of $\left|a\right|$ and period $\frac{360°}{\left|b\right|}\text{or}\frac{2\pi }{\left|b\right|}$.

## Step 3. Evaluating period of the given function.

With the help of concept stated above, the period of the function is evaluated as:

The period of $f\left(x\right)=\frac{1}{2}\mathrm{cos}\left(3x\right)$ is $\frac{360°}{\left|3\right|}=120°$.

## Step 4. Conclusion.

The period of $f\left(x\right)=\frac{1}{2}\mathrm{cos}\left(3x\right)$ is $120°$. So, option (A) is correct.