Is sine, cosine, tangent functions odd or even?

A function is called even if its graph is symmetrical about the y_axis, odd if its graph is symmetrical about the origin.

If the domain of a function is symmetrical about the number zero, it could be even or odd, otherwise it is not even or odd.

If the requirement of symmetrical domain is satisfied than there is a test to do:

##f(-x)=f(x)## the function is even.

E.G. graph{x^2 [-10, 10, -5, 5]}

##f(-x)=-f(x)## the function is odd.

E.G. graph{x^3 [-10, 10, -5, 5]}

If ##f(-x)!=f(x) or f(-x)!=-f(x)## the function is not even or odd.

Now the answer you need:

• the function ##y=sinx## is odd, because ##sin(-x)=-sinx##

graph{sinx [-10, 10, -5, 5]}

• the function ##y=cosx## is even, because ##cos(-x)=cosx##

graph{cosx [-10, 10, -5, 5]}

• the function ##y=tanx## is odd, because

##tan(-x)=sin(-x)/cos(-x)=(-sinx)/cosx=-tanx##

graph{tanx [-10, 10, -5, 5]}