Find the values of other five trigonometric functions in Exercises 1 to 5:
1. cos x = -1/2, x lies in third quadrant.

Solution:

Given, cos x = -1/ 2

It can be written as:

sec x = 1 / cos x = 1 / ( -1/2) = -2.

Using the trigonometry identity

 sin²x + cos²x = 1

1 - (-1/2)² = sin² x

1 - (1/4) = sin² x

sin² x = 3/4

sin x = ± √3/2

Since the value of cos x in the third quadrant is negative and x lies in the third quadrant.

sin x = -√3/2

cosec x = 1/ sin x 

cosec x = 1 / -√3/2

cosec x = -2/√3

tan x = sin x/ cos x

tan x = (-√3/2)/(-1/2)

tan x = √3

cot x = 1/tan x

cot x = 1/√3

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NCERT Solutions Class 11 Maths Chapter 3 Exercise 3.2 Question 1

Find the values of other five trigonometric functions in Exercises 1 to 5: 1) cos x = -1/2, x lies in third quadrant

Summary:

Hence the required values are sin x = -√3/2, cosec x = -2/√3, sec x = -2, cot x = 1/√3, and tan x = √3