Find the values of other five trigonometric functions in Exercises 1 to 5:
5. tan x = -5/12, x lies in second quadrant

Solution:

Given that tan x = – 5/12

It can be written as

cot x = 1/tan x = - 1/(5/12) = -12/5

Using the trigonometry identity

1 + tan² x = sec²x

It can be written as 

1 + (-5/12)² = sec²x

Substituting the values

1 + 25/144 = sec²x

sec²x = ( 144 + 25 ) /144 = 169 / 144

sec x = ± 13/12

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

sec x = –13/12

We have cos x = 1 / sec x = 1/(-13/12) = -12/13.

tan x = sin x/ cos x

sin x = tan x · cos x

sin x = (-5/12) × (-12/13)

sin x = 5/13

cosec x = 1/sin x

cosec x = 1/(5/13)

cosec x = 13/5

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NCERT Solutions Class 11 Maths Chapter 3 Exercise 3.2 Question 5

Find the values of other five trigonometric functions in Exercises 1 to 5: 5) tan x = -5/12, x lies in second quadrant

Summary:

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