If sin x = 2/3 find all other trigonometric ratios

sin A = 2/3

Solution:

We have,

sin A = 2/3 ……..….. (1)

As we know, by sin definition;

sin A = Perpendicular/ Hypotenuse = 2/3 ….(2)

By comparing eq. (1) and (2), we have

Opposite side = 2 and Hypotenuse = 3

Now, on using Pythagoras theorem

perpendicular side and hypotenuse we get,

⇒ 3² = Base² + 2²

= 3² – 2²

= 9 – 4

⁼ 5

= √5

Hence, Base = √5

By definition,

cos A = Base/Hypotenuse

⇒ cos A = √5/3

Since, cosec A = 1/sin A = Hypotenuse/Perpendicular

⇒ cosec A = 3/2

And, sec A = Hypotenuse/Base

⇒ sec A = 3/√5

And, tan A = Perpendicular/Base

⇒ tan A = 2/√5

And, cot A = 1/ tan A = Base/Perpendicular

⇒ cot A = √5/2