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Example 1 - Given tan A = 4/3, find other ratios - Examples

Example 1 - Chapter 8 Class 10 Introduction to Trignometry - Part 2
Example 1 - Chapter 8 Class 10 Introduction to Trignometry - Part 3

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Example 1 Given tan A = 4/3 , find the other trigonometric ratios of the angle A Given, tan A = 4/3 (𝑠𝑖𝑑𝑒 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑡𝑜 𝑎𝑛𝑔𝑙𝑒 𝐴)/(𝑠𝑖𝑑𝑒 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑡𝑜 𝑎𝑛𝑔𝑙𝑒 𝐴) = 4/3 𝐵𝐶/𝐴𝐵 = 4/3 Let BC = 4x AB = 3x We find AC using Pythagoras Theorem In right triangle ABC Using Pythagoras theorem (Hypotenuse)2 = (Height)2 + (Base)2 (AC)2 = (BC)2 + (AB)2 (AC)2 = (4x)2 + (3x)2 (AC)2 = 16x2 + 9x2 (AC)2 = 25x2 AC = √25𝑥2 AC = 5x Now, sin A = (𝑠𝑖𝑑𝑒 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑡𝑜 𝑎𝑛𝑔𝑙𝑒 𝐴)/𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 sin A = 𝐵𝐶/𝐴𝐶 sin A = 4𝑥/5𝑥 Sin A = 4/5 Similarly, cos A = (𝑠𝑖𝑑𝑒 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑡𝑜 𝐴)/𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 cos A = 𝐴𝐵/𝐴𝐶 cos A = 3𝑥/5𝑥 cos A = 3/5 Given, tan A=4/3 cosec A = 1/sin⁡𝐴 = 1/(4/5) = 5/4 sec A = 1/cos⁡〖 𝐴〗 = 1/((3/5) ) = 5/3 cot A = 1/tan⁡𝐴 = 1/(4/3) = 3/4

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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.