Question

Find all solutions on the interval [0,2π).

sin(2r)= - (√3)/2

Answer 1

I know the rule is sin(U) = c and U = arcsin(c) + k2π or U = π -arcsin(c)+k2π.

I'm just kind of trying to figure out how to write it down correctly.

Answer 2

I have all the answers, but I don't want to break any rules. Obviously I won't be working with anything +k2π, because that would be outside of the interval.

I got:

r=4π/3 + π or r= 5π/3 +π as my answers. I didn't use the second rule, because they produced answers that weren't equal to -√3/2.

Answer 3

Would I just write it in set builder notation as {r|r=4π/3 +π and r=5π/6+π}?