Tangent Calculator

Tangent calculator is used to find the tangent ratio of an acute angle (x) of a right triangle. Tangent (x) is

perpendicular/base. Tan(x) depends on the angle x.

Tan(x) = perpendicular/base = y/x

Tan(x) = sin(x) / cos(x)

Cot(x) = 1 / tan(x)

Cot (x) = base/perpendicular = x/y



Example 1: If tanA =√3, find other trigonometric ratios of angleA.

In a triangle ABC, angleB=90?

Then tanA = BC/AB = √3/1

BC = √3k and AB = k

By Pythagoras theorem we have

AC² = (AB²+BC²) = k² + (√3k)² = (k²+3k²) = 4k²

AC = √4k² = 2k

sinA = BC/AC = √3k/2k = √3/2; cosA = AB/AC = k/2k = 1/2;

cosecA = 1/sinA = 2/√3; secA = 1/ cosA = 2 and cotA = 1/tanA = 1/√3



Example 2: If 3 tan (x) = 4, evaluate (3 sin(x) + 2 cos(x)) / (3 sin(x) – 2 cos(x))
 
3 tan (x) = 4 ; tan (x) = 4 /3
 
3 sin(x) + 2 cos(x)       3 sin(x)/cos(x) + 2 cos/cos(x)         3 tan(x) + 2        3 x 4/3 + 2
---------------------  =          -----------------------------------         =  -------------     =  ------------      = 6/2 = 3
3 sin (x) – 2 cos (x)     3 sin(x)/cos(x) – 2 cos(x)/cos(x)     3 tan(x) – 2         3 x 4/3 – 2

Answer : 3