if csc (t) = 3 and t is in the second quadrant, evaluate sin (pi - t).

i know sin (t) = 1/3, and that the arcsin (1/3) gives me t, so i can just plug it in to sin (pi - t) to find that it is 1/3. positive since it is sin in quad 2. but there must be a way to do it by hand (not using arcsin function from calculator).

Question

if csc (t) = 3 and t is in the second quadrant, evaluate sin (pi - t).

i know sin (t) = 1/3, and that the arcsin (1/3) gives me t, so i can just plug it in to sin (pi - t) to find that it is 1/3. positive since it is sin in quad 2. but there must be a way to do it by hand (not using arcsin function from calculator).

anonymous · Answer

doesn't matter what quadrant you are in 
it is always true that 
$$\sin(\pi-x)=\sin(x)$$

anonymous · Answer

because pi is 180?

anonymous · Answer

|dw:1314802804901:dw|

anonymous · Answer

you should put degrees out of your mind when working with radians.   like going to another country where they use  different money. don't convert, just work with what you have

anonymous · Answer

sorry the picture is so childish. the point is that you are the same height on the unit circle, so the y - coordinate is the same

anonymous · Answer

hmm.. i guess that makes sense. but could i get a step by step explanation of the drawing. its kind of hard to understand just showing it all at once :(