Ex 8.1, 5 - Chapter 8 Class 10 Introduction to Trignometry (Term 1)

Transcript

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