If Sin x = Cos 500, then x equals

You can do this using the calculator here (I assume the 500 is 500°)

$${\mathtt{x}} = \underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}^{\!\!\mathtt{-1}}{\left(\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}{\left({\mathtt{500}}^\circ\right)}\right)} \Rightarrow {\mathtt{x}} = -{\mathtt{50.000\: \!000\: \!000\: \!002^{\circ}}}$$

This is a fourth quadrant value.  Could also have a third quadrant value:

x = 180°+50° = 230°

Check:

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left(-{\mathtt{50}}^\circ\right)} = -{\mathtt{0.766\: \!044\: \!443\: \!119}}$$

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{230}}^\circ\right)} = -{\mathtt{0.766\: \!044\: \!443\: \!119}}$$

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}{\left({\mathtt{500}}^\circ\right)} = -{\mathtt{0.766\: \!044\: \!443\: \!119}}$$

(-50° can also be written as 310°)

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{310}}^\circ\right)} = -{\mathtt{0.766\: \!044\: \!443\: \!119}}$$