Question

Given that tan ∅=-1/2, lies in quad 4 and sin α=-4/5, α lies in quad 3 find...

1. cos 2∅
2. sin 2α

Answer 1

3)

we know that θ is the IV quadrant, well, there the sine(y) is negative and the cosine(x) is positive, we have a tangent(sine/cosine) of -1/2, so one of those is the negative, in the IV Quadrant it has to be the sine, so the 1 is negative, so the fraction is (-1)/2.

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4)

recall that the hypotenuse is just a length unit, and is never negative, therefore on that sine ratio of opposite/hypotenuse, the negative is the 4, so the fraction is really (-4)/5,

also let's recall that the cosine(x) is also negative in the III Quadrant.

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