Trigonometry math questions

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1. Find cos theta if sin theta=2/3 assuming the terminal side of the angle falls in Quadrant2. Show work. 

2. Find sin theta if tan theta=1/7 assuming the terminal side of the angle falls in Quadrant 1. Show work.
May 21st, 2015

1. cos^2 (theta) + sin^2 (theta) = 1

cos^2 (theta) =1 -  sin^2 (theta) 

cos (theta) = sqrt(1 -  sin^2 (theta))

cos (theta) = sqrt(1 - (2/3)^2) = sqrt(1 - 4/9) = sqrt(5/9) = sqrt(5)/3

2. sin (theta) = sqrt(1 - cos^2 (theta)) = tan (theta)/sqrt(1 + tan^2 (theta))

sin (theta) = [1/7] / sqrt(1 + (1/7)^2) = [1/7] / sqrt(1 + 1/49) = [1/7] / sqrt(50/49) = [1/7] / [5sqrt(2)/7] = 1/5sqrt(2) = sqrt(2)/10

May 21st, 2015

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May 21st, 2015
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May 21st, 2015
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