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Q. 43PA

Expert-verifiedFound in: Page 768

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.**

**$\left(A\right)120{}^{\circ}\left(B\right)180{}^{\circ}\left(C\right)360{}^{\circ}\left(D\right)720\xb0$**

The period of** $f\left(x\right)=\frac{1}{2}\mathrm{cos}\left(3x\right)$ is $120\xb0$. So, option (A) is correct.**

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

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 $\frac{360\xb0}{\left|b\right|}\text{or}\frac{2\pi}{\left|b\right|}$.

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 $\frac{360\xb0}{\left|3\right|}=120\xb0$.

The period of $f\left(x\right)=\frac{1}{2}\mathrm{cos}\left(3x\right)$ is $120\xb0$. So, option (A) is correct.

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