SOLUTION: Find the acute angle theta that satisfies the given equation. Give theta in both degrees and radians. You should do these problems without a calculator. I know the answer to the pr

Algebra ->  Trigonometry-basics -> SOLUTION: Find the acute angle theta that satisfies the given equation. Give theta in both degrees and radians. You should do these problems without a calculator. I know the answer to the pr      Log On


   

Question 914727: Find the acute angle theta that satisfies the given equation. Give theta in both degrees and radians. You should do these problems without a calculator. I know the answer to the problem is 30 degrees= pi/6, but I don't know how to get there.
Problem: sin theta = 1/2
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

sin+%28theta%29+=+1%2F2

There are usually two answers for questions like these, so you look at special triangles where sin theta is positive, in this case, the first and second quadrants.
A special triangle with sin+%28theta%29+=+1%2F2 is a 30 - 60 - 90 triangle, with the reference angle being 30.
Thus, your answers are 30, and 180+-+30, so 30 and 150 degrees are your answers.
in radians:
theta+=+pi%2F6+%2B+2pi%2Ak or 5pi%2F6+%2B+2pi%2Ak+ where k is an integer