SOLUTION: Find the general solutions to the equation {{{csc^2theta+6csc(theta)+5=0}}}. List all solutions on the interval [0,4pi]

Algebra ->  Trigonometry-basics -> SOLUTION: Find the general solutions to the equation {{{csc^2theta+6csc(theta)+5=0}}}. List all solutions on the interval [0,4pi]      Log On


   

Question 683501: Find the general solutions to the equation csc%5E2theta%2B6csc%28theta%29%2B5=0. List all solutions on the interval [0,4pi]
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
List all solutions on the interval [0,4pi]
csc^2theta+6csc(theta)+5=0
csc%5E2x%2B6cscx%2B5=0
(cscx+5)(cscx+1)=0
cscx+5=0
cscx=-5
sinx=1/cscx=-1/5
x≈3.343,6.081,9.626,12.635 (in quadrants III and IV where sin<0)
or
cscx+1=0
cscx=-1
sinx=1/cscx=-1
x=3π/2 and 7π/2