Identities also exist to relate the value of a trigonometric
function at a given
angle to the value of that
function at the opposite of the
given angle. Here are these identities:
Any function
f
for which the equation
f (- x) = - f (x)
holds true is called an
odd function. A function for which the equation
f (- x) = f (x)
holds true
is called an even function.
Sine and
cosine are examples of odd and
even functions, respectively. Odd and even functions, by definition, reflect
themselves across the origin and y-
axis, respectively. That is, a segment whose
endpoints are
f (x)
and
f (- x)
of an odd function will always contain the
origin, whereas a segment with the same endpoints on an even function will
always be perpendicular to the
y
-axis.