Question

Given tan A = 4\3, find the other trigonometric ratio of the angle A

Answer 1

In triangle ABC given tan A is 4/3
hence opposite side is 4x, adjacent side is 3x
then by Pythagoras theorem hypotenuse will be 5x.
now,
sin A is 4/5
cos A is 3/5
cosec A is 5/4
sec A is 5/3
cot A is 3/4.

Answer 2

Answer:

Concept: using the formulae $H^{2} =A^{2} +B^{2}$

Given:  tan A =4/3

To find: other trigonometry ratios of the angle A

Step-by-step explanation:

let use the right angle triangle  to find the other trigonometric  ratios .

in a right angle triangle , one side is hypotenuse( which is called "h"), other side which is the opposite side of the hypotenuse ( which is called "a")

and the base ( which is called" b").

so, the equation of the triangle is $H^{2} =A^{2} +B^{2}$ .

given tan A = 4/3 ,  if we place the value in the right angle triangle , we will  get the the opposite side of the hypotenuse i.e. a= 4x.

and the base i.e.  b=3x.

now , placing the values in the formulae,

or, $H^{2} =A^{2} +B^{2}$

or, $H^{2} =4^{2} +3^{2}$

or, $H^{2} =16+9$

or, $H=\sqrt{25}$

or, $h=5$

so the hypotenuse is 5.

now the other trigonometric angles are

sin A = 4/5

cos a= 3/5

cosec a= 5/4

sec a= 5/3

cot a= 3/4

#SPJ3

#SPJ3