Find all solutions of the given equation Enter your answers

Find all solutions of the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to two decimal places where appropriate.) 2 sin(theta) + 1 = 0 theta = rad

Solution

2 sin theta + 1 = 0

subtracting 1 from both sides

2 sin theta = -1

sin theta = -1/2

theta = sin^-1 (-1/2)

theta = 7pi/6 + 2pik , theta= 11pi/6 + 2pik

theta = (7pi/6 + 2pik , 11pi/6 + 2pik) rad