Is tangent even or odd?
Answer: For a tangent function, f(−x) = −f(x), so tangent can be said to be an odd function.
Go through the explanation to understand better.
tan(x) = sin(x) / cos(x)
cos(x) = cos(−x)
sin(x) = −sin(−x)
Using these values in the tangent function, we get:
sin(x) / cos(x) = −sin(−x) / cos(−x) = −tan(−x)
Dividing the equation tan(x) = −tan(−x) by −1 gives
−tan(x) = tan(−x)
Thus, we see f(-x) = -f(x) which is a property of odd function.
Thus tangent can be given the form f(−x) = −f(x), so tangent can be said to be an odd function.