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| 1. |
Iif sin A3÷4find cos and tana |
| Answer» We have,{tex} \\sin A = \\frac { \\text { Perpendicular } } { \\text { Hypotenuse } } = \\frac { 3 } { 4 }{/tex}So, we draw a triangle ABC, right angled at B such that,BC = 3 units ,\xa0AC = 4\xa0units.By Pythagoras theorem, we have{tex} A C ^ { 2 } = A B ^ { 2 } + B C ^ { 2 }{/tex}{tex} \\Rightarrow \\quad 4 ^ { 2 } = A B ^ { 2 } + 3 ^ { 2 }{/tex}{tex} \\Rightarrow \\quad A B ^ { 2 } = 4 ^ { 2 } - 3 ^ { 2 }{/tex}{tex} \\Rightarrow \\quad A B ^ { 2 } = 7{/tex}{tex} \\Rightarrow \\quad A B = \\sqrt 7 {/tex}When we consider the trigonometrical-ratios of\u200b{tex} \\angle A{/tex}\u200b\u200b\u200b\u200b\u200b\u200b , we have :-Base = AB = 4 units, Perpendicular = BC = 3 units, Hypotenuse = AC = 5 units{tex} \\therefore \\quad \\cos A = \\frac { \\text { Base } } { \\text { Hypotenuse } } = \\frac { 4 } { \\sqrt 7}{/tex}\xa0and,\xa0{tex}\\quad \\tan A = \\frac { \\text { Perpendicular } } { \\text { Base } } = \\frac { 3 } { 4 }{/tex} | |