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Finding Value of trignometric functions, given other functions
Finding Value of trignometric functions, given other functions
Last updated at Feb. 12, 2020 by Teachoo
Example 7 If cotβ‘π₯ = β 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 + ((β5)/12)^2 = cosec2 x 1 + 25/144 = cosec2 x (144 + 25)/144 = cosec2 x 169/144 = cosec2x cosec2 x = 169/144 cosec2 x = 169/144 cosec x = Β± β(169/144) cosec x = Β± 13/12 As x is in llnd Quadrant, sin x is positive in llnd Quadrant, β΄ cosec x is positive in llnd Quadrant β΄ cosec x = ππ/ππ sin x = 1/cosππβ‘π₯ = 1/(13/12) = ππ/ππ tan x = 1/(πππ‘ π₯) = 1/((β5)/12) = (βππ)/π tan x = sinβ‘π₯/cosβ‘π₯ cos x = sinβ‘π₯/tanβ‘π₯ = 12/13 Γ (β5)/12 = (βπ)/ππ