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I am given that, for π/2 < x < π, sin x = 2/√13

a) Find Cos x

b) Find tan 2 x

So, what I did was: I drew a triangle and found that the missing side was equal to 3. From then, I deduced that cos x was equal to 3/√13

The problem was however that the angle must lie between the values given above. What I did was I simply added a negative sign. Is that right?

For part b I did sin 2 x / cos 2 x = tan 2 x and solved. Is that right? I got a negative answer too, which makes sense in terms of the unit circle.

Thanks,

Peter