The restrictions mean that #theta# is in the second quadrant.
Hence, sine will be positive and cosine will be negative.
The expansion of #sin2theta# will be #2sinthetacostheta#, following the double angle identity. So, we need to determine the value of #sintheta#.
Recall that #costheta= "adjacent"/"hypotenuse"#, so #"adjacent" = -24# and #"hypotenuse" = 25#. By pythagorean theorem, we have that:
#o^2 + (-24)^2 = 25^2#, where the side opposite #theta = o#
#o^2 = 625 - 576#
#o^2 = 49#
#o = +-7#
However, we know that in quadrant 2, sine is positive, so the positive answer is the correct one.
Now, recall that #sintheta = "opposite"/"hypotenuse" = 7/25#
Therefore, we can calculate #sin2theta# as the following:
#sin2theta = 2sinthetacostheta = 2(7/25)(-24/25) = -336/25#
Hopefully this helps!
