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Ex 3.2, 1 Find the values of other five trigonometric functions if cos⁑π‘₯ = – 1/2 , x lies in third quadrant. Since x is in 3rd Quadrant sin and cos will be negative But, tan will be positive Given cos x = (βˆ’1)/2 We know that sin2 x + cos2 x = 1 sin2 x + ((βˆ’1)/2)^2 = 1 sin2 x + 𝟏/πŸ’ = 1 sin2 x = 1 – 1/4 sin2 x = (4 βˆ’ 1)/4 sin2x = πŸ‘/πŸ’ sin x = ±√(3/4) sin x = Β± βˆšπŸ‘/𝟐 Since x is in 3rd Quadrant And, sin x is negative in 3rd Quadrant ∴ sin x = βˆ’βˆšπŸ‘/𝟐 Finding tan x tan x = sin⁑π‘₯/cos⁑π‘₯ = (βˆ’βˆš3/2)/((βˆ’1)/2) = (βˆ’βˆš3)/2 Γ— 2/(βˆ’1) = βˆšπŸ‘ Finding cot x cot x = 1/tan⁑π‘₯ = 𝟏/βˆšπŸ‘ Finding sec x sec x = 1/cos⁑π‘₯ = 1/((βˆ’1)/2) = (βˆ’2)/1 = βˆ’2 Finding cosec x cosec x = 1/sin⁑π‘₯ = 1/((βˆ’βˆš3)/2) = (βˆ’πŸ)/βˆšπ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 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.