Example 7 - If cot x = -5/12 , x lies in second quadrant - Examples

  1. Chapter 3 Class 11 Trigonometric Functions
  2. Serial order wise
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Example 7 If cot⁑π‘₯ = – 5/12 , x lies in second quadrant, find the values of other five trigonometric functions. Since x lies in llnd Quadrant Where cos x and tan x will be negative But sin x will be Positive we know that 1 + cot2x = cosec2 x 1 + ((βˆ’5)/12)^2 = cosec2 x 1 + 25/144 = cosec2 x (144 + 25)/144 = cosec2 x 169/144 = cosec2x cosec2 x = 169/144 cosec x = Β± √(169/144) cosec x = Β± 13/12 As x is in llnd Quadrant, sin x is positive in llnd Quadrant, cosec x is positive in llnd Quadrant ∴ cosec x = 13/12 sin x = 1/cos𝑒𝑐⁑π‘₯ = 1/(13/12) = 12/13 tan x = 1/(π‘π‘œπ‘‘ π‘₯) = 1/((βˆ’5)/12) = (βˆ’12)/5 tan x = sin⁑π‘₯/cos⁑π‘₯ cos x = sin⁑π‘₯/tan⁑π‘₯ = 12/13 Γ— (βˆ’5)/12 = (βˆ’5)/13 sec x = 1/cos⁑π‘₯ = (βˆ’13)/5

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