# How do you find the amplitude, period and graph y=5costheta?

Apr 18, 2017

Amplitude = $5$
Period = $2 \pi$
Graph:
graph{ y = 5 cos x [-10.25, 9.75, -4.92, 5.08]}

#### Explanation:

1. Amplitude is basically the maximum value $y$ can have.
Here $y = 5 \cos x$.
Max value of $\cos x = 1$
Thus, max value of $y$ is $5$.
2. Period of a function is defined as $f \left(x\right) = f \left(x + t\right)$, where t is the period of function $f \left(x\right)$. It is basically a value after which the graph repeats itself.
For the give function $y = 5 \cos x$, the period is $2 \pi$.
As $\cos \left(x\right) = \cos \left(2 \pi - x\right)$.
You can see from the graph below the fuctions repeats at $2 \pi$ intervals.
3. Graph:

graph{ y = 5 cos x [-10.25, 9.75, -4.92, 5.08]}