Finding Value of trigonometric functions, given other functions

Last updated at April 16, 2024 by

Let’s take an example

 

If cos x = –12/13 lies in second quadrant, find value of other five trigonometric functions

Since x is in 2nd Quadrant,

Finding Value of trigonometric functions, given other functions (Rough 1).jpg

tan and cos will be negative

But sin will be positive

 

Given cos x = –12/13

 

We know that

sin 2 x  +  cos 2 x = 1

sin 2 x  +  (-12/13) 2 = 1

sin 2 x  +  144/169 = 1

sin 2 x = 1 – 144/169

sin 2 x = (169 – 144)/169

sin 2 x = 25/169

sin x = ±√(25/169)

sin x = ±√25 / √169

sin x = ± 5/13

 

Since, x is in 2nd Quadrant

sin x is positive

∴ sin x = 5/13

 

Finding Value of trigonometric functions, given other functions - Part 2

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Transcript

Let s take an example If cos x = 12/13 lies in second quadrant, find value of other five trigonometric functions Since x is in 2nd Quadrant, tan and cos will be negative But sin will be positive Given cos x = 12/13 We know that sin2 x + cos2 x = 1 sin2 x + (-12/13)2 = 1 sin2 x + 144/169 = 1 sin2 x = 1 144/169 sin2 x = (169 144)/169 sin2 x = 25/169 sin x = (25/169) sin x = 25 / 169 sin x = 5/13 Since, x is in 2nd Quadrant sin x is positive sin x = 5/13

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo