Amplitude, Period, Maximum and Minimum of Trigonometric Functions
If
is a basic trigonometric function –
or
– then
- has period
ifis
or
and period
ifis
- has maximum value of 1 and minimum value of -1 ifisorandhas no maximum or minimum value ifis
The transformation of graph rules are applied in the usual way. This is illustrated above for
This means that the maximum and minimum values of
are
and
respectively, and the period of
is
the frequency is
The period and frequency of each curve above are the same since the coefficient of
is the same. The normal transformation rules apply. Adding 1 to sin x moves the curve up 1 and subtracting
from x moves the curve right
