# Is sine, cosine, tangent functions odd or even?

Feb 28, 2015

The concepts of odd and even apply only to integers .

Except for a very few special angles the values of the sine, cosine , and tangent functions are non-integer .

Mar 1, 2015

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:

$f \left(- x\right) = f \left(x\right)$ the function is even.

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

$f \left(- x\right) = - f \left(x\right)$ the function is odd.

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

If $f \left(- x\right) \ne f \left(x\right) \mathmr{and} f \left(- x\right) \ne - f \left(x\right)$ the function is not even or odd.

• the function $y = \sin x$ is odd, because $\sin \left(- x\right) = - \sin x$

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

• the function $y = \cos x$ is even, because $\cos \left(- x\right) = \cos x$

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

• the function $y = \tan x$ is odd, because

$\tan \left(- x\right) = \sin \frac{- x}{\cos} \left(- x\right) = \frac{- \sin x}{\cos} x = - \tan x$

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

Mar 10, 2018

Even

#### Explanation:

y = cos x is always going to be even, because cosine is an even function.

For example, cos$\frac{\pi}{4}$ in the first quadrant is a positive number and cos$- \frac{\pi}{4}$ (same as cos$\frac{\pi}{4}$) in the fourth quadrant is also positive, because cosine is positive in quadrants 1 and 4, so that makes it an even function. (When comparing even and odd function, use quadrants 1 and 4, if the function is positive in both quadrants, then it is even. If the function is positive in 1 and negative in 4, then it is odd)