SOLUTION: Given tan(A) = {{{ 2 }}} and A is found in Quadrant 1, find sin(2A). A.) {{{ 0 }}} B.) {{{ 1 }}} C.) {{{ 1/2 }}} D.) {{{ 4/5 }}}

Algebra ->  Test -> SOLUTION: Given tan(A) = {{{ 2 }}} and A is found in Quadrant 1, find sin(2A). A.) {{{ 0 }}} B.) {{{ 1 }}} C.) {{{ 1/2 }}} D.) {{{ 4/5 }}}      Log On


   

Question 1065402: Given tan(A) = +2+ and A is found in Quadrant 1, find sin(2A).
A.) +0+
B.) +1+
C.) +1%2F2+
D.) +4%2F5+
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Given tan(A) = 2 and A is found in Quadrant 1, find sin(2A).
By definition tan = y/x; so y = 2 and x = 1 in QI
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r = sqrt[x^2+y^2] = sqrt[2^2+1^2] = sqrt(5)
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sin(A) = y/r = 2/sqrt(5)
cos(A) = x/r = 1/sqrt(5)
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Ans:: sin(2A) = 2*sin(A)cos(A) = 2*2/sqrt(5)*1/sqrt(5) = 4/5
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Cheers,
Stan H.
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A.) +0+
B.) +1+
C.) +1%2F2+
D.) +4%2F5+