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Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


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Ex 3.2, 4 Find the values of other five trigonometric functions if sec x = 13/5 , π‘₯ 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 βˆ’ 25)/25 tan2x = 144/25 tan x = Β± √(144/25) tan x = Β± 𝟏𝟐/πŸ“ Since x is in lVth Quadrant tan x is negative in lVth Quadrant ∴ tan x = (βˆ’πŸπŸ)/πŸ“ cot x = 1/tπ‘Žπ‘›β‘π‘₯ = 1/(" " (βˆ’12)/5) = (βˆ’πŸ“)/𝟏𝟐 tan x = sin⁑π‘₯/cos⁑π‘₯ sin x = (tan x) Γ— (cos x ) = (βˆ’12)/5 Γ— 5/13 = (βˆ’πŸπŸ)/πŸπŸ‘ cos x = 1/s𝑒𝑐⁑π‘₯ = 1/(" " 13/5) = πŸ“/πŸπŸ‘ cosec x = 1/sin⁑π‘₯ = (βˆ’πŸπŸ‘)/𝟏𝟐 Ex 3.2, 5 Find the values of other five trigonometric functions if tan⁑π‘₯ = βˆ’5/12 , π‘₯ 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 + ((βˆ’5)/12)^2 = sec2x 1 + 25/144 = sec2x (144 + 25)/144 = sec2x 169/144 = sec2x sec2x = 169/144 sec2x = πŸπŸ”πŸ—/πŸπŸ’πŸ’ sec x = Β± √(169/144) sec x = Β± πŸπŸ‘/𝟏𝟐 As x is in llnd Quadrant, cos x is negative in IInd quadrant

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.