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Home >> Trigonometry Ratios >> Examples

## Find ratio of Sin, Cosec, Cos, Sec, Tan and Cot - Trigonometry : Solved Examples

 T Ratios of Angles - 30, 45, 60 & 90 degree angles Find Height, Distance using T - Ratios

If Cot Θ = 3/5, find Cosec Θ and Sec Θ
Lets draw the right angle triangle with the above mentioned details

Given thing are
Cot Θ = 3/5

we know that Cot Θ = Adjacent Side / Opposite Side, so we get

Opposite Side = 3

Hypotenuse : BC = ?
Opposite Side : AC = 3 (Opposite to ∠ Θ)

To find the Hypotenuse : BC , we use Pythagoras theorem ((Hypotenuse)2 = (Leg 1)2 + (Leg 2)2)

 __________ BC = √ AB2 + AC2

 _______ BC = √ 52 + 32

 _______ BC = √ 25 + 9

 __ BC = √ 34

Now we will try to simplify square root of 34. As no pairs can be made the final value will be

 __ BC = √ 34

So Cosec, Sec and Cot will be as follows -

Cosec Θ = Hypotenuse / Opposite Side
 ___ Cosec Θ = √ 34  / 3

Sec Θ = Hypotenuse / Adjacent Side
 ___ Sec Θ = √ 34  / 5

Cot Θ = Adjacent Side / Opposite Side
Cot Θ = 5 / 3

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