Question

I need help, I don't remember what to do.
Find all solutions of the equation in the interval [0,2pi].
(2cosè+sqrt3)(cscè+1)=0

Write your answer in radians in terms of pi.
If there is more than one solution, separate them with commas.

Answer 1

zero if either
2 cos e + sqrt 3 = 0
or if
csc e = -1

for the first (in quadrants 2 and 3 for - cos)
cos e = - sqrt 3/2
that in degrees is 180-30 or 180+30
in radians it is pi +/- pi/6

for the second sin is - so quadrants 3 and 4)
1/sin e = -1
sin e = -1
pi/2 and -pi/2

Answer 2

thanks!