Find the values of other five trigonometric functions in Exercises 1 to 5:
2. sin x = 3/5, x lies in second quadrant

Solution:

Given, sin x = 3/5

It can be written as

cosec x = 1 / sin x = 1 / (3/5) = 5/3.

Using the trigonometry identity sin²x + cos²x = 1

1 - (3/5)² = cos² x

1 - (9/25) = cos² x

cos² x = 16/25

cos x = ± 4/5

Since x lies in the second quadrant, the value of cos x is negative.

So

cos x = -4/5

sec x = 1/ cos x 

sec x = 1 / -4/5

sec x = -5/4

tan x = sin x/ cos x

= (3/5)/(-4/5)

= -3/4

cot x = 1/tan x

= 1/(-3/4)

= -4/3

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NCERT Solutions Class 11 Maths Chapter 3 Exercise 3.2 Question 2

Find the values of other five trigonometric functions in Exercises 1 to 5: 2) sin x = 3/5, x lies in second quadrant

Summary:

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