Question

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

Answer 1

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

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