If cos⁡ x=5/13, and 0°<x<90° is in Quadrant I, what is tan⁡(2x)?

Question

Enter your answer as a fraction in simplest form, like this: 3/14

Answer 1

If cos x = 5/13 and x is between 0 and 90 degrees, since we know that tan2x = sin2x/cos2x = (2 sinxcosx)/(cos^2x - sin^2x) and we are dealing with a 5-12-13 right triangle,

tan (2x) = 2(12/13)(5/13)/((5/13)^2 - (12/13)^2) = (2*12*5/13^2) / (25/13^2) - (144/13^2)= 120/(-119)= -1.008403

Answer 2

Hi Raquel,

There's a double angle formula for tan(2x). It's a special case of the formula for the tangent of the sum of 2 angles: tan(x+y) = [tan(x) + tan(y)] / [1 - tan(x)tan(y)]. Just set x = y and you will have it!