SOLUTION: If sin x = 1/2 and x is in the first quadrant, find tan2x

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Question 669543: If sin x = 1/2 and x is in the first quadrant, find tan2x

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
If sin+%28x+%29=+1%2F2, then 2sin+%28x%29=+1
we are looking for tan%282x%29
use identity: tan2x+=%282+cos%28x%29+sin%28x%29%29%2F%28cos%5E2%28x%29-sin%5E2%28x%29%29
plug in sin+%28x+%29=+1%2F2

tan%282x%29+=%282+cos%28x%29+%281%2F2%29%29%2F%28cos%5E2%28x%29-%281%2F2%29%5E2%29

use identity: cos%5E2%28x%29=1-sin%5E2%28x%29 and cos%28x%29=sqrt%281-sin%5E2%28x%29%29



tan2x+=%28sqrt%281-%281%2F2%29%5E2%29%29%2F%281-%281%2F2%29%5E2-%281%2F2%29%5E2%29

tan2x+=sqrt%281-1%2F4%29%2F%281-1%2F4-1%2F4%29

tan2x+=sqrt%283%2F4%29%2F%281-2%2F4%29

tan2x+=%28sqrt%283%29%2F2%29%2F%282%2F4%29
tan2x+=4sqrt%283%29%2F4
tan2x+=cross%284%29sqrt%283%29%2Fcross%284%29
tan2x+=sqrt%283%29
tan2x+=1.73