Question

Which of the six trigonometric functions are odd? And which are even? Justify the answers using trigonometric identities and graphs.​

Answer 1

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 only if f(-x) = f(x) and is symmetric to the y axis. It is helpful to know if a function is odd or even when you are trying to simplify an expression when the variable inside the trigonometric function is negative.

sin( -x ) = - sin x

csc ( -x ) = - csc x

cos ( -x ) = cos x

sec (-x ) = sec x

tan ( -x ) = - tan x

tan ( -x ) = - cot x

Answer 2

Step-by-step explanation:

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