Trig
posted by Jon .
Find the exact value of sin2(theta) if cos(theta) = sqrt 5/3 and 180 < theta < 270.
A)1/9
B)4 sqrt 5/9
C)1/9
D)4 sqrt 5/9
B?
sin^2(theta) + cos^2(theta) = 1
sin^2(theta) = 1  cos^2(theta)
sin^2(theta) = 1  (sqrt 5/3)^2
sin^2(theta) = 1  (sqrt 25/9)

You are getting a lot of these wrong lately.
(I am going to use sinx for your sin(theta)
since cosx = √5 /3
using Pythagoras I found the other side ot the triangle to be 2.
But we are in the third quadrant so sinx =2/3
then sin 2x = 2sinxcosx
= 2(2/3)(√5/3)
= 4√5/3 which is D
with a calculator, you could have easily checked that your choice and the others beside D would not work. 
oops, sorry type
make 4√5/3 which is D
read : 4√5/9 which is D 
I really thought I had that one.
My 1st thought was D but I figured since sqrt 5/3 was negative then so would my final answer. 
Are you familiar with the CAST rule, that is, do you know which ratios are negative in which quadrants??

No