A graph is given with a plot of y = sin(x) for 0 <= x <= 360. Which value of x in the range 90 <= x <= 180 satisfies sin(x) = sin(30)?

x = 150.This question requires that the student uses the symmetry of the sine graph. If we draw y = sin(30) on top of y = sin(x), it is clear that a possible value of x is 150.
A harder question could use a transformation of sin(x). E.g. which values in the range 90 <= x <= 360 satisfy sin(x) = -sin(30) (Ans: x = 210, x = 330).The student could draw y = -sin(30), and use the fact that this line meets the curve y = sin(x) 30 degrees from the point where y = sin(x) meets the x axis.