Find the solution set of sin x = csc x in the interval (0°, 360°). [Answer(s) should be correct to the nearest degree.]

We must find just the solutions that belong to the range
(0 , 2pi).

We'll recall the identity csc x = 1/sin x and
we'll substitute csc x by the equivalent ratio, into the given
identity.

sin x = 1/sin
x

We'll multiply by sin x both
sides:

(sin x)^2 - 1 = 0

We'll
recognize the difference of squares:

(sin x - 1)(sin x + 1)
= 0

We'll cancel each
factor:

sin x = 1 => x = pi/2 radians or 90
degrees.

sin x = -1 => x = 3pi/2 radians or 270
degrees.

The solutions of the equation in
degrees, over the range (0 , 360) are: {90, 270}.