Ex 8.1, 5
Given sec θ =13/12, calculate all other trigonometric ratios.
Finding cos θ
cos θ = 1/secθ
cos θ = 𝟏𝟐/𝟏𝟑
Now,
cos θ = 12/13
(𝑠𝑖𝑑𝑒 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑡𝑜 ∠𝜃)/𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 = 12/13
𝑨𝑩/𝑨𝑪=𝟏𝟐/𝟏𝟑
Let
AB = 12x
AC = 13x
Using Pythagoras theorem to find BC
(Hypotenuse)2 = (Height)2 + (Base)2
AC2 = AB2 + BC2
(13x)2 = (12x)2 + (BC)2
(BC)2 = (13x)2 − (12x)2
(BC) 2 = 169x2 – 144x2
(BC) 2 = 25x2
BC = √(25𝑥^2 )
BC = √(5^2 𝑥^2 )
BC = 5x
Now, finding other ratios
sin θ = (𝑠𝑖𝑑𝑒 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑡𝑜 ∠𝜃)/𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
= 𝐵𝐶/𝐴𝐶
= 5𝑥/13𝑥
= 𝟓/𝟏𝟑
tan θ = (𝑠𝑖𝑑𝑒 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑡𝑜 ∠𝜃)/(𝑠𝑖𝑑𝑒 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑡𝑜 ∠𝜃)
= 𝐵𝐶/𝐴𝐵
= 5𝑥/12𝑥
= 𝟓/𝟏𝟐
cosec 𝛉 = 1/sinθ
= 1/((5/13) )
= 𝟏𝟑/𝟓
cot θ = 1/tanθ
= 1/((5/12) )
= 𝟏𝟐/𝟓

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo

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