Expert: Ahmed Salami - 10/16/2004

Question
PointA(1/2,sqrt(3)/2) is on the unit circle whose center is the origin. If theta is an angle in standard position whose terminal ray passes through A, what is the value of sin of theta?

Answer
Hi Jeff,
Due to the fact that i'm unable to provide you with any kind of sketch, i think it'll be good if you tried sketching the situation to enable you understand what the question requires.
Anyway,the value of sin of theta would be the length of the x coordinate at that point divided by the length of the diagonal of the right-angle triangle containing the angle which happens to be the radius of the circle . A unit circle has a radius of 1 unit. Therefore,
sin# = [sqrt(3)/2]/1
    = sqrt(3)/2
In case you're interested, the angle would then be 60 degrees.

Regards.