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