Question 33858
cos(x) = adj/hyp
sin(x) = opp/hyp
tan(x) = opp/adj<br>
We are given that cos(x) = 5/12 so we can use 5 for the adjacent side and 12 for the hypotenuse. By the Pythagorean Theorem, {{{(adj)^2 + (opp)^2 = (hyp)^2}}} so:
{{{5^2 + (opp)^2 = 12^2}}}
Simplifying we get:
{{{25 + (opp)^2 = 144}}}
Subtracting 25 from each side we get:
{{{(opp)^2 = 119}}}
Finding the square root of each side we get:
{{{abs(opp) = sqrt(119)}}}
Since tan(x) is negative and tan(x) is opp/hyp and the hypotenuse is always positive, the opposite side must be negative. So:
{{{opp = -sqrt(119)}}}
and so, since sin(x) = opp/hyp:
{{{sin(x) = (-sqrt(119))/12}}}