SOLUTION: I have been given this equation and solution but I am not understanding a specific step in the solution. CSC theta = -2 solution 1/sin theta = -2 (do not understand this

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Question 1035420: I have been given this equation and solution but I am not understanding a specific step in the solution.
CSC theta = -2
solution
1/sin theta = -2
(do not understand this step)
sin theta = -1/2
How does the equation steps look?
I need the steps of how to get the 1/sin to sin and -2 to -1/2.
Thank you
Found 2 solutions by Alan3354, MathTherapy:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
I have been given this equation and solution but I am not understanding a specific step in the solution.
CSC theta = -2
solution
1/sin theta = -2
(do not understand this step)
sin theta = -1/2
How does the equation steps look?
=============
If you want to solve the equation for theta:
CSC theta = -2
1/csc = sin = 1/-2
csc = 1/sin for all angles.
--> sin(theta) = 1/-2 = -1/2
----
You can use a calculator to find theta = -30 degs
--> 330 degrees, or 210 degrees since sine is negative in Q3 and Q4

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
I have been given this equation and solution but I am not understanding a specific step in the solution.
CSC theta = -2
solution
1/sin theta = -2
(do not understand this step)
sin theta = -1/2
How does the equation steps look?
I need the steps of how to gethe 1/sin to sin and -2 to -1/2.
Thank you
csc+%28theta%29+=+-+2

1%2Fsin+%28theta%29+=+-+2 ------- Substituting matrix%281%2C3%2C+1%2Fsin+%28theta%29%2C+for%2C+csc+%28theta%29%29 

-+2+%2A+sin+%28theta%29+=+1 ----- Cross-multiplying

sin+%28theta%29+=+-+1%2F2 ------- Dividing by - 2



You didn't specify a range, but matrix%281%2C3%2C+sin+%2830%5Eo%29+=+1%2F2%2C+or%2C+sin+%28theta%29+=+pi%2F6%29, but since sin+%28theta%29+%3C+0, 

then theta is in the 3rd and 4th quadrants (matrix%281%2C5%2C+7pi%2F6%2C+and%2C+11pi%2F6%2C+%22%2C%22%2C+respectively%29), where sin is < 0 (negative).