Trig Functions: Unit Modes
The trig functions evaluate differently depending on the units
on q. For example, sin(90°) = 1, while sin(90)=0.89399....
If there is a degree sign after the angle, the trig function
evaluates its parameter as a degree measurement. If there
is no unit after the angle, the trig function evaluates its
parameter as a radian measurement. This is because
radian measurements are considered to be the "natural" measurements
for angles. (Calculus gives us a justification for this. A parital
explaination comes from the formula for the area of a circle sector,
which is simplest when the angle is in radians).

Calculator note: Many calculators have **degree**, **radian**, and
**grad** modes (360° = 2p rad = 400 grad). It is important to have the calculator in the
right mode since that mode setting tells the calculator which
units to assume for angles when evaluating any of the trigonometric
functions. For example, if the calculator is in degree mode,
evaluating sine of 90 results in __1__. However, the calculator
returns __0.89399...__ when in radian mode. Having the calculator
in the wrong mode is a common mistake for beginners, especially
those that are only familiar with degree angle measurements.

For those who wish to reconcile the various trig functions
that depend on the units used, we can *define* the degree symbol
(°) to be the value (PI/180). Therefore, sin(90°),
for example, is really just an expression for the sine
of a radian measurement when the parameter is fully evaluated.
As a demonstration, sin(90°) = sin(90(PI/180))
= sin(PI/2). In this way, we only need to tabulate the
"natural" radian version of the sine function.
(This method is similar to defining percent % = (1/100)
in order to relate percents to ratios, such as 50% = 50(1/100) = 1/2.)