Ex 3.2, 5 - Chapter 3 Class 11 Trigonometric Functions

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Ex 3.2, 5 Find the values of other five trigonometric functions if tan⁡𝑥 = −5/12 , 𝑥 lies in second quadrant. Since x lies in llnd Quadrant So, sin x will be positive But tan x and cos x will be negative We know that 1 + tan2x = sec2x 1 + ((−5)/12)^2 = sec2x 1 + 25/144 = sec2x (144 + 25)/144 = sec2x 169/144 = sec2x sec2x = 169/144 sec2x = 𝟏𝟔𝟗/𝟏𝟒𝟒 sec x = ± √(169/144) sec x = ± 𝟏𝟑/𝟏𝟐 As x is in llnd Quadrant, cos x is negative in IInd quadrant So, sec x is negative in llnd Quadrant ∴ sec x = (−𝟏𝟑)/𝟏𝟐 cos x = 1/s𝑒𝑐⁡𝑥 = 1/((−13)/12) = (−𝟏𝟐)/𝟏𝟑 tan x = sin⁡𝑥/cos⁡𝑥 tan x × cos x = sin x sin x = tan x × cos x = (−5)/12 × (−12)/13 = 𝟓/𝟏𝟑 cosec x = 1/𝑠𝑖𝑛⁡𝑥 = 1/(5/13) = 𝟏𝟑/𝟓 cot x = 1/(𝑡𝑎𝑛 𝑥) = 1/((−5)/12) = (−𝟏𝟐)/𝟓