My question is in from Jan/08 #1 Part 1
Solve for theta over the interval (0,2pi), to decimal places
2csc2θ +cscθ −10=0
*the first step to solving this equation is to factor it so that there is 2csctheat+5 in one bracket and csctheta-2 in the other bracket
*to solve 2csctheta+5, you get the csctheta by itself which will give you -5/2 on the other side. Then you flip the fraction (-2/5) to solve for sine, and the reference angle to 3 decimal points is 0.411.Theta then equals 3.553, 5.871 because sine is positive in quadrants 3 and 4.
*in the next bracket get csc theta by itself, making the other side equal to 2 or 2/1. Flip the fraction to solve the reference angle for sine (1/2). You will notice that sin=1/2 at pi/6. sin is positive in quadrants 1 and 2 in this question making your answer pi/6, 5pi/6.