Are you sure the question is , not ?
If it is, then no value of x can satisfy that equation.
Find the solutions to the following equations in the interval [0,2 ].
(c) sin2x=−23 .
Note. sin2x means sin(2x) and not (sin2)x.
Hint. The angle x belongs to the interval [0,2 ] if and only if the angle 2x belongs to the interval [0,4 ]. So, how many solutions does the given equation have in the interval [0,2 ] ?
What is this asking? I got 4pi/3 and 5p/3 but it's obviously not right.
Also the title should obviously be sin 2x not cos..
Addition to what mathaddict had explained :
Because sin is periodic with period ,where n is integer, the value of sin (2x) will be the same as . Then :
1. for n = 1
. So : ----> find x
2. for n = 2
. So ....
Continue until finding all values of x that satisfy the equation
Or you can use formula (general solution for sin) :
, where n is integer
1) for n = 0
----> we reject this
2) for n = 1