How do you graph to solve the equation on the interval #[-2pi,2pi]# for #cscx=-(2sqrt3)/3#?

1 Answer
Feb 1, 2017

Answer:

#-pi/3, (-2pi)/3, (4pi)/3, (5pi)/3#

Explanation:

#csc x = 1/(sin x) = - (2sqrt3)/3#
#sin x = - 3/(2sqrt3) = - sqrt3/2#
Use trig table of special arcs and unit circle:

For interval #(- 2pi, 0)#, there are 2 answers:
#sin x = - sqrt3/2# --> #x = - pi/3# and #x = (-2pi)/3#
For interval #(0, 2pi)#, there are 2 answers:
sin x = - sqrt3.2 ---> #x = (4pi)/3# and #x = (5pi)/3#