Trig
posted by Bob on .
find all solutions to the equation √3 csc(2theta)=2
Would the answer be
π/6 + 2πn, 5π/6 +2πn or π/6 + πn, 5π/6 +πn?
or neither?

sqrt ( 3 ) * csc ( 2 theta ) =  2 Divide both sides by sqrt ( 3 )
csc ( 2 theta ) =  2 / sqrt ( 3 )
Take the inverse cosecant of both sides.
2 theta =  pi / 3
and
2 theta = 4 pi / 3
[ Becouse csc ( pi / 3 ) = 2 / sqrt ( 3 ) , and csc ( 4 pi / 3 = 2 / sqrt ( 3 ) ]
Divide both sides by 2
theta =  pi / 6
and
theta = 2 pi / 3
Period of csc ( theta ) = 2 pi
So period of 2 theta = 2 pi / 2 = pi
Final solutions :
theta = n pi + 2 pi / 3 = pi ( n + 2 / 3 )
and
theta = n pi  pi / 6 = pi ( n  1 / 6 )