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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 Cosec Θ = 5/7, find Sec Θ and Cot Θ
Lets draw the right angle triangle with the above mentioned details

Given thing are
Cosec Θ = 5/7

we know that Cosec Θ = Hypotenuse / Opposite Side, so we get

Opposite Side = 5
Hypotenuse = 7

Hypotenuse : BC = 7
Opposite Side : AC = 5 (Opposite to ∠ Θ)

To find the Adjacent Side - AC , we use Pythagoras theorem ((Hypotenuse)2 = (Leg 1)2 + (Leg 2)2)

 __________ AB = √ BC2 - AC2

 _______ AB = √ 72 - 52

 _______ AB = √ 49 - 25

 __ AB = √ 24

Now we will try to simplify square root of 24 and we get (2 x 2 x 2 x 3). Take out pairs and we get

 ______ AB = 2 √ 2 x 3

 __ AB = 2 √ 6

So Cosec, Sec and Cot will be as follows -

Cosec Θ = Hypotenuse / Opposite Side
Cosec Θ = 7 / 5

Cot Θ = Adjacent Side / Opposite Side
 _ Cot Θ = 2 √ 6  / 5

Sec Θ = Hypotenuse / Adjacent Side
 _ Sec Θ = 7 / 2 √ 6

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