If I pick a point on a graph with coordinates (5,-5) the angle formed between the x-axis and the hypotenuse can be either $-45^\circ$ or $315^\circ$ (along with all multiples of $360^\circ$). Yes?

If this is true, then I would think that $\sin(-45^\circ) = \sin(315^\circ) = \dfrac{-\sqrt{2}}{2}$

If I plot the sine function I see that $\sin(-45^\circ) = \dfrac{-\sqrt{2}}{2}$ but my calculator gives me an error when entering $\sin(-45^\circ)$ or $\sin(\dfrac{-\pi}{4})$

Likewise, my current lesson on complex numbers requires that I use the sin and cos functions of $\dfrac{7\pi}{4}$ rather than $\dfrac{-\pi}{4}$

I would appreciate an explanation of when to use a negative reference angle and when to use the positive angle $< 360^\circ$