**Trigonometric ratios csc sec and cot :**

In the right triangle, we refer to the lengths of the three sides according to how they are placed in relation to the angle **θ**

- The side that is opposite to the right angle is called the Hypotenuse. This is the longest side in a right triangle.
- The side that is opposite to the angle
**θ**is called the Opposite side. - The side that runs alongside the angle
**θ**and which is not the Hypotenuse is called the Adjacent side.

We can form six ratios with the sides of a right triangle.

sin **θ = **Opposite side / Hypotenuse side

cos θ = Adjacent side / Hypotenuse side

tan θ = Opposite side / Adjacent side

cosec θ = Hypotenuse side / Opposite side

sec θ = Hypotenuse side / Adjacent side

tan θ = Adjacent side / Opposite side

**Example 1 :**

Find the csc ∠B, sec ∠B, cot ∠B

**Solution :**

cosec θ is the reciprocal of sin θ, sec θ is the reciprocal of cos θ like that cot θ is the reciprocal of tan θ.

BC = hypotenuse side = 17

AB = opposite side = 8

AC = Adjacent side = 15

cosec ∠B:

Hypotenuse side/opposite side ==> BC/AB ==> 17/8

sec ∠B:

Hypotenuse side/Adjacent side ==> BC/AC ==> 17/15

cot ∠B:

Adjacent side/Opposite side ==> AC/AB ==> 15/8

**Example 2 :**

Find the Cosec ∠A, sec ∠A and cot ∠A

**Solution :**

cosec θ is the reciprocal of sin θ, sec θ is the reciprocal of cos θ like that cot θ is the reciprocal of tan θ.

AC = hypotenuse side = 65

BC = opposite side = 33

AB = Adjacent side = 56

cosec ∠A :

Hypotenuse side/opposite side ==> AC/BC ==> 65/33

sec ∠A :

Hypotenuse side/Adjacent side ==> AC/AB ==> 65/56

cot ∠A :

Adjacent side/opposite side ==> AB/BC ==> 56/33

**Example 3 :**

Find the tan ∠B

**Solution :**

cosec θ is the reciprocal of sin θ, sec θ is the reciprocal of cos θ like that cot θ is the reciprocal of tan θ.

BC = hypotenuse side = 5

AC = opposite side = 4

AB = Adjacent side = 3

cosec ∠A :

Hypotenuse side/opposite side ==> BC/AC ==> 5/4

sec ∠A :

Hypotenuse side/Adjacent side ==> BC/AB ==> 5/3

cot ∠A :

Adjacent side/opposite side ==> AB/AC ==> 3/4

After having gone through the stuff given above, we hope that the students would have understood "Trigonometric ratios csc sec and cot".

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