Calculate cos x, using right angled triangles, if sin x = b/a. Solution The value of the sine function, in a right angle triangle, is found from the ratio between the opposite cathetus, to the angle, and the hypotenuse. From the enunciation, sin x = b/a, so we\'ll conclude that opposite cathetus is b and the hypotenuse is a. cos x = joined cathetus/hypotenuse = joined cathetus/a Also, in a right angle triangle, by applying Pythagorean theorem, we\'ll have: (hypotenuse a)^2=(cathetus b)^2 + (cathetus c)^2 (a)^2 = b^2 + c^2 c^2 = (a)^2 - (b)^2 c = [(a)^2 - (b)^2]^1/2 cos x =[(a^2 - b^2)^1/2]/a.