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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 6 If cosβ‘π₯ = β 3/5 , x lies in third quadrant, find the values of other five trigonometric functions. Since x is in lllrd Quadrant sin and cos will be negative But tan will be positive Given cos x = (β3)/5 We know that sin2 x + cos2 x = 1 sin2 x + ((β3)/5)^2 = 1 sin2 x + 9/25 = 1 sin2 x = 1 β 9/25 sin2 x = (25 β 9)/25 sin2 x = (25 β 9)/25 sin2x = 16/25 sin x = Β±β(16/25) sin x = Β± 4/5 Since, x is in lllrd Quadrant And sin x is negative lllrd Quadrant β΄ sin x = βπ/π tan x = sinβ‘π₯/cosβ‘π₯ = (β 4/5)/(β 3/5) = (β4)/5 Γ 5/(β3) = π/π cot x = 1/tanβ‘π₯ = 1/(4/3) = π/π cosec x = 1/sinβ‘π₯ = 1/(β 4/5) = (βπ)/π sec x = 1/cosβ‘π₯ = 1/((β3)/5) = 5/(β3) = (βπ)/π