If csc(ϴ) = 6, find the exact value if sin(2 ϴ)?

1 Answer
Apr 2, 2018

Please see below.

Explanation:

Without more information we can only answer

#sin2 theta = +-sqrt35/18#

Recall that #sin2 theta = 2sintheta cos theta#.

So we want both #sin theta# and #cos theta#.

#csc theta = 6# tells us that #1/sin theta = 6#

so that #sin theta = 1/6#.

Now, using #sin^2 theta +cos^2 theta = 1#, we get

#cos theta = +-sqrt35/6#

Therefore,

#sin2 theta = 2sintheta cos theta#.

# = 2(1/6)(+-sqrt35/6)#

# = +- sqrt35/18#