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Home / 08 Trigonometric Functions / 11 Trigonometry and Even vs Odd Functions

As a reminder:

Even Functions: Opposite inputs result in the same output: \(f(-x) = f(x)\).

Odd Functions: Opposite inputs result in opposite outputs: \(f(-x) = -f(x)\).

Are Sine/Cosine/Tangent even, odd, or neither?

Pick some angles on the unit circle and compare:

\(\cos(\theta)\) vs. \(\cos(-\theta)\)

\(\sin(\theta)\) vs. \(\sin(-\theta)\) and

\(\tan(\theta)\) vs. \(\tan(-\theta)\).


Solution

Cosine is Even: \(\cos(-\theta)=\cos(\theta)\)

Sine is Odd:\(\sin(-\theta)=-\sin(\theta)\)

Tangent is Odd: \(\tan(-\theta)=-\tan(\theta)\)