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Ex 3.2, 4 - Find values of other five functions if sec x = 13/5

Ex 3.2, 4 - Chapter 3 Class 11 Trigonometric Functions - Part 2
Ex 3.2, 4 - Chapter 3 Class 11 Trigonometric Functions - Part 3

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Transcript

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± 12/5 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

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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.