Solve The Following Equation in the Interval [0, 2pi]?

Question

I am having a little trouble with this math problem. I am assuming that it is asking at what angle(s) "t" does sin = 1/2 ? I tried 1pi/6 and 5pi/6, because sin equals 1/2 at both of those angles. Here is a link to the specific question I am referring to:

http://img374.imageshack.us/img374/7403/picture1qt9.jpg

Thanks alot for your help!

Answer 1

So the question says:

(sin t)^2 = 1/2

so we take the square root of both sides and get:

sin t = + or - (sqrt of 2)/2

well where does sin equal sqrt(2)/2 (both positive and negative)  well according to the unit circle, you would get:

pi/4, 3pi/4, 5pi/4, 7pi/4

Voila

Answer 2

the question,

(sint(t))^2 = 1/2

first, take the square roots of both sides and get

sin(t)=+sqrt(1/2) and -sqrt(1/2)

now you are asked at what angles sin(t) = plus or minus sqrt(1/2)

this happens at four angles, when t=pi/4, 3 pi/4, 5 pi/4 and 7 pi/4