Question

If tanA =4/3,then find the values of sin A and cos A

Answer 1

here is your answer

Answer 2

Given: tan A =4/3

To find The values of sin A and cos A

Solution: If we consider a right-angled triangle, it has three parts perpendicular(or height), base, and hypotenuse.

In trigonometric functions,

sin A= perpendicular/hypotenuse

cos A= base/hypotenuse

tan A= perpendicular/base

∴ tan A= perpendicular/base=4/3

So perpendicular=4 and base=3

Using Pythagoras theorem, we have

(hypotenuse)²= (perpendicular)²+(base)²

⇒ (hypotenuse)²= (4)²+(3)²  [substituting the values from above]

⇒ (hypotenuse)²=16+9

⇒ (hypotenuse)²=25

⇒ hypotenuse = 5  [taking square root on both sides]

∴ sin A= perpendicular/hypotenuse = 4/5

cos A= base/hypotenuse = 3/5

Hence the values of sin A and cos A are 4/5 and 3/5 respectively.