Question 615576
<ol><li>For {{{tan(2theta)}}} we have the formula:
{{{tan(2theta) = 2tan(theta)/(1-tan^2(theta))}}}</li><li>For the formula we need {{{tan(theta)}}}</li><li>For {{{tan(theta)}}} we need the opposite side, the adjacent side and the quadrant that {{{theta}}} terminates in. We're given the quadrant.</li><li>Since {{{sin(theta) = 4/5}}} and since sin is opposite over hypotenuse, we can use 4 for the opposite side and 5 for the hypotenuse.</li><li>We can use the 4 and the 5 and the Pythagorean Theorem to find the adjacent side. (Be sure to put the 4, the 5 and your variable in the correct places in the equation. Hint: The hypotenuse is <i>always</i> the longest side in a right triangle.)</li><li>Form {{{tan(theta)}}} by putting the opposite side, 4, over the adjacent side you just figured out. (And since {{{theta}}} terminates in the 1st quadrant, we will use the positive ration of opposite over adjacent).)</li><li>Take the {{{tan(theta)}}} you just got and put it in the two spots for {{{tan(theta)}}} in
{{{tan(2theta) = 2tan(theta)/(1-tan^2(theta))}}}
and simplify.</li></ol>