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Finding Value of trignometric functions, given other functions
Finding Value of trignometric functions, given other functions
Last updated at May 29, 2023 by Teachoo
Ex 3.2, 1 Find the values of other five trigonometric functions if cos𝑥 = – 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 = (−1)/2 We know that sin2 x + cos2 x = 1 sin2 x + ((−1)/2)^2 = 1 sin2 x + 𝟏/𝟒 = 1 sin2 x = 1 – 1/4 sin2 x = (4 − 1)/4 sin2x = 𝟑/𝟒 sin x = ±√(3/4) sin x = ± √𝟑/𝟐 Since x is in 3rd Quadrant And, sin x is negative in 3rd Quadrant ∴ sin x = −√𝟑/𝟐 Finding tan x tan x = sin𝑥/cos𝑥 = (−√3/2)/((−1)/2) = (−√3)/2 × 2/(−1) = √𝟑 Finding cot x cot x = 1/tan𝑥 = 𝟏/√𝟑 Finding sec x sec x = 1/cos𝑥 = 1/((−1)/2) = (−2)/1 = −2 Finding cosec x cosec x = 1/sin𝑥 = 1/((−√3)/2) = (−𝟐)/√𝟑