We know that $$\cos(45^{\circ})=\sin(45^{\circ})=\frac{\sqrt{2}}{2}$$
But when I type this in Maple and use it in my calculations, I get a different result compared to when I use $\frac{\sqrt{2}}{2}$. For example:
$$31\sin(45^{\circ})=26.37$$
$$31\cdot \frac{\sqrt{2}}{2}=21.92$$
Perhaps this is a dumb question, but is there something I need to change in my settings?
On
As everyone has mentioned, MAPLE works with radians. If you are feeling particular lazy, Maple has a convert to radians procedure: convert(x, radians) will convert x to radians, where x is of the form "15degrees" (i.e. a number immediately followed by degrees).
If you wanted, you could also write a trivial function SIN(x) that would take degrees as an argument, something along the lines of:
SIN:= unapply( sin(x*Pi/180), x);
Similar can be done for the other trig functions.
Maple does not work with degrees. If you want to take $\sin$ of $45^{\circ}$ in Maple you would write
$$ \sin\left(45 \frac{\pi}{180}\right) $$
to get the correct result.