# Trigonometric Ratios

In a right-angled triangle ABC.

Let, AB = p

BC = b

AC = h

We define the six trigonometrical ratios as shown under,

sin

cos Î¸ = cosine q =

tan Î¸ = tangent Î¸ =

cosecant Î¸ = cosec Î¸ =

secant Î¸ = sec Î¸ =

cotangent Î¸ = cot Î¸ =

**Note 1**

From the above definitions we observe that,

cosec Î¸ = , sec Î¸ = , cot Î¸ =

**Note 2**

cosec Î¸ is defined when sin Î¸ â‰ Î¸, sec Î¸ is defined when cos Î¸ â‰ 0 and cot Î¸ is defined when

tan Î¸ â‰ 0.

**Note 3**

Maximum value of sin Î¸ = 1 when Î¸ = 90Â°, Maximum value of cos Î¸ = 1 when Î¸ = 0 and the maximum value of tan Î¸ is not defined.

**Problem 1**:

Example

Find the values of sec A and cot A, if tan C =
Solution

Consider a Î” ABC, right angled at B,

As it is given that, tan C = .

Therefore, if , where k is a positive number.

Now, by using the Pythagoras theorem,

Using the definitions of trigonometric ratios we have to find the values of sec A and cot A.

Thus sec A = and cot A = .