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Finding Value of trignometric functions, given other functions
Finding Value of trignometric functions, given other functions
Last updated at Sept. 3, 2021 by Teachoo
Ex 3.2, 4 Find the values of other five trigonometric functions if sec x = 13/5 , π₯ lies in fourth quadrant. Since x lies in the lVth Quadrant Where cos will be positive But sin and tan will be negative We know that 1 + tan2x = sec2x 1 + tan2x = (13/5)^2 tan2x = (13/5)^2β 1 tan2x = 169/25 β 1 tan2x = (169 β 25)/25 tan2x = 144/25 tan x = Β± β(144/25) tan x = Β± 12/5 Since x is in lVth Quadrant tan x is negative in lVth Quadrant β΄ tan x = (βππ)/π cot x = 1/tππβ‘π₯ = 1/(" " (β12)/5) = (βπ)/ππ tan x = sinβ‘π₯/cosβ‘π₯ sin x = (tan x) Γ (cos x ) = (β12)/5 Γ 5/13 = (βππ)/ππ cos x = 1/sππβ‘π₯ = 1/(" " 13/5) = π/ππ cosec x = 1/sinβ‘π₯ = (βππ)/ππ