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Finding Value of trignometric functions, given other functions
Finding Value of trignometric functions, given other functions
Last updated at Jan. 4, 2022 by Teachoo
Ex 3.2, 1 Find the values of other five trigonometric functions if cosβ‘π₯ = β 1/2 , x lies in third quadrant. Since x is in 3rd Quadrant sin and cos will be negative But, tan will be positive Given cos x = (β1)/2 We know that sin2 x + cos2 x = 1 sin2 x + ((β1)/2)^2 = 1 sin2 x + π/π = 1 sin2 x = 1 β 1/4 sin2 x = (4 β 1)/4 sin2x = π/π sin x = Β±β(3/4) sin x = Β± βπ/π Since x is in 3rd Quadrant And, sin x is negative in 3rd Quadrant β΄ sin x = ββπ/π Finding tan x tan x = sinβ‘π₯/cosβ‘π₯ = (ββ3/2)/((β1)/2) = (ββ3)/2 Γ 2/(β1) = βπ Finding cot x cot x = 1/tanβ‘π₯ = π/βπ Finding sec x sec x = 1/cosβ‘π₯ = 1/((β1)/2) = (β2)/1 = β2 Finding cosec x cosec x = 1/sinβ‘π₯ = 1/((ββ3)/2) = (βπ)/βπ