Question 872997
{{{sin(theta) = 3/5}}}



{{{sin^2(theta) = (3/5)^2}}}



{{{sin^2(theta) = 9/25}}}



{{{1-sin^2(theta) = 1-9/25}}}



{{{1-sin^2(theta) = 25/25-9/25}}}



{{{1-sin^2(theta) = 16/25}}}



{{{cos^2(theta) = 16/25}}}



{{{cos(theta) = -sqrt(16/25)}}} Note: because {{{pi/2 < theta < pi}}}, this means {{{theta}}} is in quadrant II (where cosine is negative)



{{{cos(theta) = -4/5}}}



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{{{tan(theta) = (sin(theta))/(cos(theta))}}}



{{{tan(theta) = ((3/5))/((-4/5))}}}



{{{tan(theta) = ((3/5))*((-5/4))}}}



{{{tan(theta) = (3*(-5))/(5*4)}}}



{{{tan(theta) = -15/20}}}



{{{tan(theta) = -3/4}}}



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{{{tan(2theta) = (2*tan(theta))/(1 - tan^2(theta))}}}



{{{tan(2theta) = (2*(-3/4))/(1 - (-3/4)^2)}}}



{{{tan(2theta) = (2*(-3/4))/(1 - 9/16)}}}



{{{tan(2theta) = (2*(-3/4))/(16/16 - 9/16)}}}



{{{tan(2theta) = (2*(-3/4))/(7/16)}}}



{{{tan(2theta) = (-6/4)/(7/16)}}}



{{{tan(2theta) = (-3/2)/(7/16)}}}



{{{tan(2theta) = (-3/2)*(16/7)}}}



{{{tan(2theta) = (-3*16)/(2*7)}}}



{{{tan(2theta) = (-48)/(14)}}}



{{{tan(2theta) = -24/7}}}