Question

How do you graph `y=cos(x+pi/2)`?

Answer 1

Shift points on the graph of `y=cos(x)` to the left by `pi/2` units, plot a full period, and plot further using the fact that cosine is periodic and reflected over the y-axis if necessary.

Explanation:

Shift some points on the graph of `y=cos(x)` to the left `pi/2` units (subtract `pi/2` from the x-coordinate) .

`(0,1)` becomes `(-pi/2,1)`
`(pi/2,0)` becomes `(0,0)`
`(pi,-1)` becomes `(pi/2,-1)`
`((3pi)/2,0)` becomes `(pi,0)`
`(2pi,1)` becomes `((3pi)/2,1)`

Plotting these points will yield a full period for `y=cos(x+pi/2)`. From `((3pi)/2,1)`, the graph repeats itself. graph{y=cos(x+pi/2) [-10, 10, -5, 5]}

Also, recall that `cos(x)` is an even function ( `cos(-x)=cos(x)`) , meaning it has y-axis symmetry. Reflect these points over the y-axis to obtain a larger portion of the graph for negative values of `x.`