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Transcript

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

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, Social Science, Physics, Chemistry, Computer Science at Teachoo.