# How do you find the period, amplitude and sketch y=2+1/10cos60pix?

Nov 19, 2017

See below.

#### Explanation:

Period:

The period of $\cos x = 2 \pi$

Multiplying $x$ by $60 \pi$ causes a compression by a factor of $\frac{1}{60 \pi}$

So period is $\frac{1}{60 \pi} \cdot 2 \pi = \frac{1}{30}$ radians

The amplitude of $\cos x = 1$

Multiply by $\frac{1}{10}$ causes a reduction by a factor of 10.

So $\frac{1}{10} \cdot 1 = \frac{1}{10}$

This is increased by 2, because the function has had 2 added to it, which translates the curve in the positive y direction by 2 units.

So amplitude is:

$\frac{1}{10} + 2 = \frac{21}{10} = 2.1$

The stretch is a compression in this case by a factor of $\frac{1}{60 \pi}$

$\therefore$

Period is $\textcolor{b l u e}{\frac{1}{30}}$ radians

Amplitude is $\textcolor{b l u e}{2.1}$

Stretch is $\textcolor{b l u e}{\frac{1}{60 \pi}}$

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