Consider the graph of the function y = sin x + cos x.

Question

Consider the graph of the function y = sin x + cos x. Describe its overall shape.

1. Is it periodic?
2. How do you know?

Answer 1

A function is periodic if f(x+a)=f(x) for some value of a.

You need to show that sin(x+a)+cos(x+a)=sin(x)+cos(x) for some a.

Expand the left side and work the algebra down to prove it and find the value of a that you need.