Question

How do you know where to plot the points of a cosine function on a graph? Is there a more simple way then plugging the x value into the calculator?

Answer 1

nope.

Although you do know that the period is 2π, so it crosses the x-axis at intervals of π, with

cos(0) = 1
cos(π/2) = 0
cos(π) = -1
cos(3π/2) = 0
cos(2π) = 1

Then sketch a smooth curve using those points. If you want other points, you can use known values at π/6, π/4, π/3 and their multiples.

Most other points you will need to use your calculator.