The function f(x) = sin(x) is an odd function. The function g(x)=cos(x) is an even function. How do the graphs of the functions show that?

Question

How does the unit circle and the circular definition of the two functions show that?

Answer 1

Sin (x) is an odd function because Sin(-x) = - Sin (x). If you look at the graph of Sinx, observe that

Sin (π/2) = 1, and Sin(-π/2) = -1. Hence , an odd function.

Cosx is an even function because cos(-x) = + cos(x).. In the graph of cos x, observe that

Cos (π/4) = (1/√2), and cos (-π/4) also = (1/√2). Hence an even function.