Question

If tan A = 3/4, then find the other trigonometric ratio of angle A.

Answer 1

tan A = perpendicular/base=3/4
So P=3x and B=4x(let).
By Pythagoras theorem the H =5x.
So sin A =3/5,
cos A=4/5,
cot A=4/3
cosec A=5/3
secA=5/4

Answer 2

Given tan A = 3/4

Hence tanA = opposite side to A/Adjacent side to A = 3/4

Let us take,

The opposite side as BC=3k and the adjacent side as AB=4k.(where k is any positive number)

Now, In triangle ABC

By pythagoras theorem,

AC^2 = AB^2+BC^2

AC^2 = (3K)^2+(4K)^2

AC^2 = 9K^2+16K^2

AC^2 = 25K^2

AC = Square root of 25k^2

AC = 5k(hypotenuse)

The other trigonometric ratios are:

SinA = opposite side to A/hypotenuse = 3k/5k = 3/5

CosA = Adjacent side to A/hypotenuse = 4k/5k = 4/5

CosecA = 1/sinA = 1/3/5 = 5/3

SecA = 1/cosA = 1/4/5 = 5/4

CotA = 1/tanA = 1/3/4 = 4/3