Ex 3.2, 2 - Chapter 3 Class 11 Trigonometric Functions

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Ex 3.2, 2 Find the values of other five trigonometric functions if sin x = 3/5 , x lies in second quadrant. Since x is in llnd Quadrant sin will be positive But cos and tan will be negative Here , sin x = 3/5 We know that sin2x + cos2x = 1 (3/5)^2 + cos2x = 1 9/25 + cos2x = 1 cos2x = 1 – 9/25 cos2x = 𝟏𝟔/𝟐𝟓 cos x = ±√(16/25) cos x = ± 𝟒/𝟓 As x is llnd Quadrant cos x is negative llnd Quadrant ∴ cos x = (−𝟒)/𝟓 Now, tan x = sin⁡𝑥/cos⁡𝑥 = (3/5)/(− 4/5) = 3/5 × 5/(−4) = (−𝟑)/𝟒 cosec = 1/sin⁡𝑥 = 1/(3/5) = 𝟓/𝟑 sec x = 1/cos⁡𝑥 = 1/(− 4/5) = (−𝟓)/𝟒 cot x = 1/tan⁡𝑥 = 1/((−3)/4) = (−𝟒)/𝟑