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

Question 683501: Find the general solutions to the equation AMP Parsing Error of [csc^2theta+6csc(theta)+5=0]: Invalid function '\theta+6\csc(theta)+5=0': opening bracket expected at /home/ichudov/project_locations/algebra.com/templates/Algebra/Expression.pm line 70. . . List all solutions on the interval [0,4pi]
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
List all solutions on the interval [0,4pi]
csc^2theta+6csc(theta)+5=0
AMP Parsing Error of [csc^2x+6cscx+5=0]: Invalid function '\x+6\cscx+5=0': opening bracket expected at /home/ichudov/project_locations/algebra.com/templates/Algebra/Expression.pm line 70. .
(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

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