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Duncan
Mathematics
18 February, 23:27
Find sin θ if cot θ = - 2 and cos θ < 0
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Kenyon Kerr
18 February, 23:35
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Given was cotθ = - 21 and cot is the reciprocal of tan
therefore
tanθ = 1 - 2
solve for the hypotenuse c since t he opposite side a=1 and the adjacent sides b=-2 were already given. that is,
c2 = a2 + b2
c = √ (1) 2 + (-2) 2
c = √5
Solving for sinθ
sinθ = oppositesides hypoteνse = ab
sinθ = 1 √5 need to rationalize
sinθ = (1 √5) * √5 √5
sinθ = √5 5
Note that the adjacent side of the angle is - 2 so the angle
θ is found in the 2nd quadrant.
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