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If sinA = 1/3 and cosA<0

find the exact value of tan2A

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sinA = 1/3 and cosA<0
find the exact value of tan2A
What quadrant is A? Sin is +, cos is - so quadrant 2, so 2 A is quadrant 3 or 4
cos^2A = 1 - sin^2A = 1-1/9 = 8/9
cos A = -(2/3)sqrt 2
tanA = (1/3)/[-(2/3)sqrt2)] = -1/(2 sqrt 2)
tan 2A = 2 [-1/(2 sqrt 2)]/[1- 1/8]
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