Example 6 - If cos x = -3/5 , x lies in third quadrant, find - Finding Value of trignometric functions, given other functions

  1. Chapter 3 Class 11 Trigonometric Functions
  2. Serial order wise
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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 sin2x = 16/25 sin x = ±√(16/25) sin x = Β± 4/5 Since, x is in lllrd Quadrant sin x is negative lllrd Quadrant ∴ sin x = βˆ’4/5 tan x = sin⁑π‘₯/cos⁑π‘₯ = (βˆ’ 4/5)/(βˆ’ 3/5) = (βˆ’4)/5 Γ— 5/(βˆ’3) = 4/3 cosec x = 1/sin⁑π‘₯ = 1/(βˆ’ 4/5) = (βˆ’5)/4 sec x = 1/cos⁑π‘₯ = 1/((βˆ’3)/5) = 5/(βˆ’3) = (βˆ’5)/3 cot x = 1/tan⁑π‘₯ = 1/(4/3) = 3/4

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