In this section, you will learn how to find the values of the trigonometric ratios csc, sec and cot.

The formulas given below can be used to find the trigonometric ratios csc, sec and cot.

csc **θ = **Hypotenuse / Opposite side

sec θ = Hypotenuse / Adjacent side

cot θ = Adjacent side / Opposite side

**Example 1 :**

In the right triangle shown below, find the values of csc B, sec B, cot B.

**Solution :**

90° is at ∠A. So the side which is opposite to 90° is known as hypotenuse. The side which is opposite to ∠B is known as opposite side. The remaining side is known as adjacent side.

So, we have

BC = Hypotenuse = 17

AC = Opposite side = 15

AB = Adjacent side = 8

Finding the value of csc B :

csc B = Hypotenuse / Opposite side

csc B = BC/AC

csc B = 17/15

Finding the value of sec B :

sec B = Hypotenuse / Adjacent side

sec B = BC/AB

sec B = 17/8

Finding the value of cot B :

cot B = Adjacent side / Opposite side

cot B = AB/AC

cot B = 8/15

**Example 2 :**

In the right triangle shown below, find the values of csc A, sec A and cot A.

**Solution :**

90° is at ∠B. So the side which is opposite to 90° is known as hypotenuse. The side which is opposite to ∠A is known as opposite side. The remaining side is known as adjacent side.

So, we have

AC = Hypotenuse = 65

BC = Opposite side = 33

AB = Adjacent side = 56

Finding the value of csc A :

csc A = Hypotenuse / Opposite side

csc A = AC/BC

csc A = 65/33

Finding the value of sec A :

sec A = Hypotenuse / Adjacent side

sec A = AC/AB

sec A = 65/56

Finding the value of cot A :

cot A = Adjacent side / Opposite side

cot A = AB/BC

cot A = 56/33

**Example 3 :**

In the right triangle shown below, find the values of csc C, sec C and cot C.

**Solution :**

90° is at ∠A. So the side which is opposite to 90° is known as hypotenuse. The side which is opposite to ∠C is known as opposite side. The remaining side is known as adjacent side.

So, we have

BC = Hypotenuse = 5

AB = Opposite side = 3

AC = Adjacent side = 4

Finding the value of csc C :

csc C = Hypotenuse / Opposite side

csc C = BC/AB

csc C = 5/3

Finding the value of sec C :

sec C = Hypotenuse / Adjacent side

sec C = BC/AC

sec C = 5/4

Finding the value of cot C :

cot C = Adjacent side / Opposite side

cot C = AC/AB

cot C = 4/3

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