find cos if sin=-1/3 and tan=>0

Question

i dont understand how to do this problem can you please help.I have a test on wedsnday. It would mean alot to me thank you. im really really struggling in pre cal

Answer 1

Given that Sin(x) = -1/3 from a calculator we find arcSin(-1/3) = -19.47 degrees.However, Tan(-19.47) < 0

Looking at the Sin function we see that Sin(x) < 0 from 180 degress to 270 degrees and the Tan > 0 in that interval

Taking Sin((180 + 19.47) we get -1/3 as expected. At 180 + 19.47 degrees the Tan = 0.35 > 0 as required.

Finally we have Cos(180 + 19.47) = -0.943.