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Ex 8.1, 5 - Given sec = 13/12, calculate other ratios. - Finding ratios when other ratio is given

Ex 8.1, 5 - Chapter 8 Class 10 Introduction to Trignometry - Part 2
Ex 8.1, 5 - Chapter 8 Class 10 Introduction to Trignometry - Part 3

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Ex 8.1, 5 Given sec θ =13/12, calculate all other trigonometric ratios. Finding cos θ cos θ = 1/sec⁡θ cos θ = 1/(13/12) 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 = (13x)2 - (12x)2 (BC) 2 = 169x2 – 144x2 (BC) 2 = 25x2 BC = √(25𝑥^2 ) BC = √(5^2 𝑥^2 ) BC = 5x sin θ = (𝑠𝑖𝑑𝑒 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑡𝑜 ∠𝜃)/𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 = 𝐵𝐶/𝐴𝐶 = 5𝑥/13𝑥 = 5/13 cos θ = 12/13 tan θ = (𝑠𝑖𝑑𝑒 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑡𝑜 ∠𝜃)/(𝑠𝑖𝑑𝑒 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑡𝑜 ∠𝜃) tan θ = 𝐵𝐶/𝐴𝐵 tan θ = 5𝑥/12𝑥 tan θ = 5/12

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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 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.