Ex 3.2, 4 - Chapter 3 Class 11 Trigonometric Functions

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Ex 3.2, 4 Find the values of other five trigonometric functions if sec x = 13/5 , 𝑥 lies in fourth quadrant. Since x lies in the lVth Quadrant Where cos will be positive But sin and tan will be negative We know that 1 + tan2x = sec2x 1 + tan2x = (13/5)^2 tan2x = (13/5)^2– 1 tan2x = 169/25 – 1 tan2x = (169 − 25)/25 tan2x = 144/25 tan x = ± √(144/25) tan x = ± 𝟏𝟐/𝟓 Since x is in lVth Quadrant tan x is negative in lVth Quadrant ∴ tan x = (−𝟏𝟐)/𝟓 cot x = 1/t𝑎𝑛⁡𝑥 = 1/(" " (−12)/5) = (−𝟓)/𝟏𝟐 tan x = sin⁡𝑥/cos⁡𝑥 sin x = (tan x) × (cos x ) = (−12)/5 × 5/13 = (−𝟏𝟐)/𝟏𝟑 cos x = 1/s𝑒𝑐⁡𝑥 = 1/(" " 13/5) = 𝟓/𝟏𝟑 cosec x = 1/sin⁡𝑥 = (−𝟏𝟑)/𝟏𝟐 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