Ex 3.2, 5 - If tan x = -5/12, find other five trignometric - Finding Value of trignometric functions, given other functions

  1. Chapter 3 Class 11 Trigonometric Functions
  2. Serial order wise
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Ex3.2, 5 Find the values of other five trigonometric functions if tan⁡𝑥 = −5/12 , 𝑥 lies in second quadrant. Since x lies in llnd Quadrant So, sin x will be positive But tan x and cos x will be negative We know that 1 + tan2x = sec2x 1 + ((−5)/12)^2 = sec2x 1 + 25/144 = sec2x (144 + 25)/144 = sec2x 169/144 = sec2x sec2x = 169/144 sec x = ± √(169/144) sec x = ± 13/12 As x is in llnd Quadrant, cos x is negative in IInd quadrant So, sec x is negative in llnd Quadrant ∴ sec x = (−13)/12 cos x = 1/s𝑒𝑐⁡𝑥 = 1/((−13)/12) = (−12)/13 cot x = 1/tan⁡𝑥 = 1/((−5)/12) = (−12)/5 tan x = sin⁡𝑥/(𝑐𝑜𝑠 𝑥) sin x = (tan x) × (cos x) = (−5)/12 × (−12)/13 = 5/13 cosec x = 1/sin⁡𝑥 = 1/(5/13) = 13/5

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