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

sin²x + cos²x = 1

sin²x  = 1 - cos²x

sin²x  = 1 - (5 / 13)²

sin² x = 1 - 25 / 169

sin²x  = (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

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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