# Find the values of other five trigonometric functions in Exercises 1 to 5:

4. sec x = 13/5, x lies in fourth quadrant

**Solution:**

Given sec x = 13 / 5

It can be written as cos x = 1 / sec x = 1 / (13 / 5) = 5 / 13.

Using the trigonometry identity

sin^{2}x + cos^{2}x = 1

sin^{2}x = 1 - cos^{2}x

sin^{2}x = 1 - (5 / 13)^{2}

sin^{2} x = 1 - 25 / 169

sin^{2}x = (169 - 25) / 169 = 144 / 169

sin x = ± 12 / 13

Since x lies in the fourth quadrant, the value of sin x is negative.

sin x = - 12 / 13.

It can be written as

cosec x = 1/ sin x

cosec x = 1 / -(12/13)

cosec x = -13/12

tan x = sin x/ cos x

tan x = (-12/13)/(5/13)

tan x = -12/5

cot x = 1/tan x

cot x = -5/12

NCERT Solutions Class 11 Maths Chapter 3 Exercise 3.2 Question 4

## Find the values of other five trigonometric functions in Exercises 1 to 5: 4) sec x = 13/5, x lies in fourth quadrant

**Summary:**

It is given that sec x = 13/5, x lies in fourth quadrant. We found the other five trigonometric functions to be sin x = -12/13, cosec x = -13/12, cos x = 5/13, cot x = -5/12, and tan x = -12/5

visual curriculum