Question

How do you graph `sin (x + (3pi)/2)`?

Answer 1

As shown below: graph{sin(x+ (3pi)/2 ) [-4.87, 5.61, -2.62, 2.62]}

Explanation:

This question concerns transformations of functions:

We recall: `f(x+alpha)` represents a transformation of `(-alpha,0)`
or `alpha` units to the left:

So `sin(x+ (3pi)/2 )` is just `sinx` shited `(3pi)/2` to the left:

`sinx` :

graph{sinx [-4.076, 4.075, -2.038, 2.038]}

`sin(x + (3pi)/2 )` :

graph{sin(x+ (3pi)/2 ) [-4.87, 5.61, -2.62, 2.62]}