Example 6 - Chapter 3 Class 11 Trigonometric Functions

Last updated at April 16, 2024 by

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Example 6 If cos⁑π‘₯ = – 3/5 , x lies in third quadrant, find the values of other five trigonometric functions. Since x is in lllrd Quadrant sin and cos will be negative But tan will be positive Given, cos x = (βˆ’3)/5 We know that sin2 x + cos2 x = 1 sin2 x + ((βˆ’3)/5)^2 = 1 sin2 x + 9/25 = 1 sin2 x = 1 – 9/25 sin2 x = (25 βˆ’ 9)/25 sin2 x = (25 βˆ’ 9)/25 sin2x = πŸπŸ”/πŸπŸ“ sin x = ±√(16/25) sin x = Β± πŸ’/πŸ“ Since, x is in lllrd Quadrant And sin x is negative lllrd Quadrant ∴ sin x = βˆ’πŸ’/πŸ“ tan x = sin⁑π‘₯/cos⁑π‘₯ = (βˆ’ 4/5)/(βˆ’ 3/5) = (βˆ’4)/5 Γ— 5/(βˆ’3) = πŸ’/πŸ‘ cot x = 1/tan⁑π‘₯ = 1/(4/3) = πŸ‘/πŸ’ cosec x = 1/sin⁑π‘₯ = 1/(βˆ’ 4/5) = (βˆ’πŸ“)/πŸ’ sec x = 1/cos⁑π‘₯ = 1/((βˆ’3)/5) = 5/(βˆ’3) = (βˆ’πŸ“)/πŸ‘

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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