Use the figure below to find all angles between 0 and 2π satisfying the given condition.
Recall that csc(θ) = is tlhXe1fkNqXdqLAu09V4zt1nrKKdBdu2
And thus, sin(θ) = is hiSbMvmJe/RtAmcjPbEVlU2Q6gjKgqAp
Since and we are given that , if follows that sin(θ)=2121aHagpiu+V7f7C0spLha8A7NBeMRa
The figure shows that in the first quadrant, when θ = 3h1r3BovJpGHdfHF1e45PgxphjpwTJo/RfpbcA==.
The only other quadrant where sin(θ) is positive is the cgdjgMwzgdsN/2V28SBxLETxfR3f1IZ8zuIV8A== quadrant.
We need a second quadrant angle, , for which .
From the figure,
θ = 5tzDXePpEG7sPma4qrPqyyLH0PD10LXs2oa5ObfsjWM=
Thus, for the following values of θ (0 < θ < 2π).
θ = 3h1r3BovJpGHdfHF1e45PgxphjpwTJo/RfpbcA== and 5tzDXePpEG7sPma4qrPqyyLH0PD10LXs2oa5ObfsjWM=