SOLUTION: Given that sin2A=1/3 and 2A is in Quadrant 2, what is the exact value of tanA?

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Question 1122762: Given that sin2A=1/3 and 2A is in Quadrant 2, what is the exact value of tanA?
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
sin%282A%29+=+1%2F3 and 2A in Q2 gives the following picture, where we can solve for the x value of -sqrt%288%29:




Now, you can use
with alpha+=+beta+:

+tan%282A%29+=+-1%2F%28sqrt%288%29%29+=+2tan%28A%29+%2F+%281-tan%5E2%28A%29%29+

which eventually (let u = tan(A), complete the square) resolves to +highlight%28+tan%28A%29+=+3+%2B+2sqrt%282%29%29+ in Q1