SOLUTION: Hi if tan theta equals 3/4 and cos theta is <0 find sin theta and cos theta as fractions. thanks

Question 1117330: Hi
if tan theta equals 3/4 and cos theta is <0 find sin theta and cos theta as fractions.
thanks
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
tan theta = sin theta / cos theta
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tan theta = 3/4 > 0 and cos theta < 0 ---> sin theta < 0
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this occurs in the third quadrant
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we can use a 3-4-5 triangle with a hypotenuse of 5 and sides -3 and -4, then
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sin theta = -3/5 and cos theta theta = -4/5
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we check this answer by noting that tan^(-1) 3/4 = 36.8699
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we have an angle in the third quadrant so 180 + 36.8699 = 216.8699
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sin 216.8699 = -0.600000033 approximately -3/5 = -0.6
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cos 216.8699 = -0.799999975 approximately -4/5 = -0.8
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our answer checks
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