Is the function y = sinx-tgx even or odd?
| August 7, 2021 | education
A function is even if the following condition is met for any of its arguments:
f (x) = f (-x).
A function is odd if equality is satisfied for any of its arguments:
f (-x) = -f (x).
f (x) = sin x – tg x.
The function is the difference between the sine and the tangent of the argument. Both trigonometric functions are odd.
Find f (-x):
f (-x) = sin (-x) – tg (-x) = -sin x – (-tg x) = tg x – sin x.
Find -f (x):
-f (x) = – (sin x – tg x) = tg x – sin x.
f (-x) = -f (x), so the function is odd.
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