Find the integer $n,$ $-90 \le n \le 90,$ such that $\sin n^\circ = \sin 1021^\circ.$
I know that the sine function is periodic, which means it repeats itself every 360 degrees. So, if I subtract 360 degrees from 1021 degrees, I will get the same sine value. That means $\sin 1021^\circ = \sin (1021 - 360)^\circ = \sin 661^\circ.$ I can keep subtracting 360 degrees until I get a number between -90 and 90, which is the range of n. So, $\sin 661^\circ = \sin (661 - 360)^\circ = \sin 301^\circ.$ And $\sin 301^\circ = \sin (301 - 360)^\circ = \sin (-59)^\circ.$ So, n = -59 is an integer that satisfies the given condition.

