Question

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

Answer 1

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`