Find the values of other five trigonometric functions in Exercises 1 to 5:
3. cot x = 3/4, x lies in third quadrant.

Solution:

Given, cot x = 3/ 4

It can be written as

tan x = 1/cot x = 1/(3/4) = 4/ 3.

Using the trigonometry identity

1 + tan²x = sec²x

It can be written using the values

1 + (4/ 3)2 = sec² x

1 + (16 / 9) = sec² x

( 9 + 16 ) / 9 = sec² x

sec² x = 25 / 9

sec x = ± 5 / 3

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

sec x = - 5 /3

cos x = 1/ sec x 

cos x = 1 / (-5/3)

cos x = -3/5

tan x = sin x/ cos x

sin x = tan x cos x

=  4/3 × (-3/5)

= -4/5

cosec x = 1/sin x

= 1/ (-4/5)

= -5/4

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NCERT Solutions Class 11 Maths Chapter 3 Exercise 3.2 Question 3

Find the values of other five trigonometric functions in Exercises 1 to 5: 3) cot x = 3/4, x lies in third quadrant.

Summary:

cot x = 3/4, x lies in third quadrant. We found the other five trigonometric functions to be  sin x = -4/5, cosec x = -5/4, cos x = -3/5, sec x = -5/3, and tan x = 4/3.