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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 Sec Θ = 11/13, find Cosec Θ and Cot Θ
Lets draw the right angle triangle with the above mentioned details

Given thing are
Sec Θ = 11/13

we know that Sec Θ = Hypotenuse / Adjacent Side, so we get

Hypotenuse = 13

Hypotenuse : BC = 13
Opposite Side : AC = ? (Opposite to ∠ Θ)

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

 ____________ AC = √ BC2 - AB2

 ____________ AC = √ 132 - 112

 ____________ AC = √ 169 - 121

 __ AC = √ 48

Now, we will simplify square root

 _________________ AC = √ 2 x 2 x 2 x 2 x 3

 __ AC = 2 + 2 √ 3   (pairs taken out)

 __ AC = 4 √ 3

So Cosec, Sec and Cot will be as follows -

Cosec Θ = Hypotenuse / Opposite Side
 __ Sin Θ = 13 / 4√ 3

Cot Θ = Adjacent Side / Opposite Side
 __ Tan Θ = 11 / 4√ 3

Sec Θ = Hypotenuse / Adjacent Side
Sec Θ = 13/11

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