Is Cosine Odd Or Even

Even and Odd Trig Functions

All functions, including trig functions, can be described as being even, odd, or neither. A function is odd if and only if f(-x) = - f(x) and is symmetric with respect to the origin. A function is even if and simply if f(-x) = f(ten) and is symmetric to the y axis. Information technology is helpful to know if a part is odd or even when you lot are trying to simplify an expression when the variable inside the trigonometric function is negative.

sin( -ten ) = - sin 10	csc ( -x ) = - csc 10
cos ( -ten ) = cos x	sec (-ten ) = sec x
tan ( -x ) = - tan x	tan ( -ten ) = - cot 10

Example 1: find the value of (4 · sin (-60))ⁱⁱ

= (-iv · sin (60))ⁱⁱ sin(-x) = - sin 10

= 12

Example ii: Decide if the following office is odd or fifty-fifty

f(x) = x^three sin x

Find f(-x) f(-ten) = -(-x)^threesin (x) replacing 10 with -x and sin (-x) = - sin ten

f(-x) = x³ sin x

f(x) = f(-x) therefore the function is fifty-fifty.

Instance iii: Make up one's mind if the graph is odd or even.

The graph is symmetric with respect to the origin therefore it is on odd function.

Cosine Function

The graph is symmetric to the y- axis therefore it is an even function.

The majority of functions are neither odd nor even, however, sine and tangent are odd functions and cosine is an even function. This can be important information when identifying graphs.