Math Lesson A Day: Prove that tan(x) = sin(x)/cos(x)

Wednesday, January 21, 2009

Prove that tan(x) = sin(x)/cos(x)

Image of a triangle with an angle x, and the opposite, adjacent, and hypotenuse, labeled

sin(x) = (0/H)

cos(x) = (A/H)

Then sin(x)/cos(x) =

(O/H)/(A/H) =

(O/H)*(H/A) =

(O/A) = tan(x)

So sin(x)/cos(x) = tan(x)