Suggested languages for you:

Americas

Europe

Q25.

Expert-verifiedFound in: Page 767

Book edition
Middle English Edition

Author(s)
Carter

Pages
804 pages

ISBN
9780079039903

**Find the amplitude if it exists and period of the function $y=4\mathrm{tan}\left(\frac{\theta}{3}\right)$** **and then graph the function.**

The amplitude of $y=4\mathrm{tan}\left(\frac{\theta}{3}\right)$ is undefined.

The period of $y=4\mathrm{tan}\left(\frac{\theta}{3}\right)$ is $3\pi $.

The given function is $y=4\mathrm{tan}\left(\frac{\theta}{3}\right)$.

A function of the form $y=a\mathrm{tan}\left(bx\right)\text{and}y=a\mathrm{cot}\left(bx\right)$ has undefined amplitude and period $\frac{180\xb0}{\left|b\right|}\text{or}\frac{\pi}{\left|b\right|}$.

With the help of concept stated above, the amplitude and period of the function $y=4\mathrm{tan}\left(\frac{\theta}{3}\right)$ is evaluated as:

The amplitude of $y=4\mathrm{tan}\left(\frac{\theta}{3}\right)$ is undefined.

The period of $y=4\mathrm{tan}\left(\frac{\theta}{3}\right)$ is $\frac{\pi}{\left|\frac{1}{3}\right|}=3\pi $.

The graph for the function $y=4\mathrm{tan}\left(\frac{\theta}{3}\right)$ is shown below.

The amplitude of $y=4\mathrm{tan}\left(\frac{\theta}{3}\right)$ is undefined.

The period of $y=4\mathrm{tan}\left(\frac{\theta}{3}\right)$ is $3\pi $.

94% of StudySmarter users get better grades.

Sign up for free