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Ex 3.2, 1 - Find values of other five trigonometric functions if cos x = -1/2 , x lies in third quadrant. - Ex 3.2

  1. Chapter 3 Class 11 Trigonometric Functions
  2. Serial order wise
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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 lllrd 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 + 1/4 = 1 sin2 x = 1 – 1/4 sin2 x = (4 βˆ’ 1)/4 sin2x = 3/4 sin x = ±√(3/4) sin x = Β± √3/2 Since, x is in lllrd Quadrant sin x is negative lllrd Quadrant ∴ sin x = βˆ’βˆš3/2 tan x = sin⁑π‘₯/cos⁑π‘₯ = (βˆ’ √3/2)/((βˆ’1)/2) = (βˆ’βˆš3)/2 Γ— 2/(βˆ’1) = √3 cosec x = 1/sin⁑π‘₯ = 1/((βˆ’βˆš3)/2) = (βˆ’2)/√3 sec x = 1/cos⁑π‘₯ = 1/((βˆ’1)/2) = (βˆ’2)/1 = -2 cot x = 1/tan⁑π‘₯ = 1/√3

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