Question

Evaluate cotθ if sinθ= √6/5

Answer 1

Answer:
`cot \theta =\sqrt{ (19)/(6) }`.

Step-by-step explanation: Given sinθ= √6/5.

We know radio of
`Sin\theta =(Opposite \ side )/(Hypotenuse)`.

Therefore,

`(Opposite \ side )/(Hypotenuse)= (√(6) )/(5)`.

Let us apply Pythagoras Theorem to find the third side(Adjacent side) of the triangle .

`(a)^2 + (b)^2 = (c)^2.`

`(√(6))^2+(b)^2=(5)^2`

`6+(b)^2 = 25`

Subtracting 6 from both sides, we get

`6-6+(b)^2 = 25-6`

`(b)^2 = 19`

`b=√(19)`

Therefore, adjacent side =
`√(19)`

We know,

`cot \theta = (Adjacent \ side)/(Opposite \ side)`

`cot \theta =(√(19) )/(√(6) )`

Or

`cot \theta =\sqrt{ (19)/(6) }`.