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What is one example of an odd trigonometric function? Show that your function meets the criteria for an odd function.
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Example: f(x) = sin x.
Odd-function test: f is odd if f(-x) = -f(x) for all x in its domain. Using the sine subtraction formula,
sin(-x) = sin(0 - x) = sin 0·cos x − cos 0·sin x = 0 − 1·sin x = −sin x.
Hence f(-x) = −f(x) for all real x, so sin x is an odd function. (Other odd trig functions include tan x, cot x and csc x on their domains.)
Odd-function test: f is odd if f(-x) = -f(x) for all x in its domain. Using the sine subtraction formula,
sin(-x) = sin(0 - x) = sin 0·cos x − cos 0·sin x = 0 − 1·sin x = −sin x.
Hence f(-x) = −f(x) for all real x, so sin x is an odd function. (Other odd trig functions include tan x, cot x and csc x on their domains.)
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