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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 is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.