Question

2 If sinA = 1/3, then find the value of cotA? + 1.​

Answer 1

Given : $\sf{\sin A = \dfrac{3}{5}}$

Need To Find : The value of cot A .

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❍ Basic Formulas of Trigonometry is given by :

$\boxed { \begin{array}{c c} \\ \dag \qquad \large {\underline {\bf{ Some \:Basic\:Formulas \:For\:Trigonometry \::}}}\\\\ \sf{ In \:a \:Right \:Angled \: Triangle-:} \\\\ \sf {\star Sin \theta = \dfrac{Perpendicular}{Hypotenuse}} \\\\ \sf{ \star \cos \theta = \dfrac{ Base }{Hypotenuse}}\\\\ \sf{\star \tan \theta = \dfrac{Perpendicular}{Base}}\\\\ \sf{\star \cosec \theta = \dfrac{Hypotenuse}{Perpendicular}} \\\\ \sf{\star \sec \theta = \dfrac{Hypotenuse}{Base}}\\\\ \sf{\star \cot \theta = \dfrac{Base}{Perpendicular}} \end{array}}$

• $\sf{\sin A = \dfrac{1}{3}= \dfrac{Perpendicular} { Hypotenuse} }$

Therefore,

• Perpendicular of Right Angled Triangle is 1 cm .

• Hypotenuse of Right angled triangle is 3 cm .

⠀⠀⠀⠀⠀Finding Base of Right angled triangle :

$\sf{\underline {\dag As, \:We \:Know\:that \::}}\\ \\ \bf{ By \:Pythagoras\:Theorem\::}$

$\underline {\boxed {\sf{\star (Perpendicular)^{2} + Base^{2}  = ( Hypotenuse)^{2} }}}$

❍ Let's Consider the Base of Triangle be x cm .

⠀⠀⠀⠀⠀⠀$\underline {\bf{\star\:Now \: By \: Substituting \: the \: Given \: Values \::}}$

⠀⠀⠀⠀⠀$:\implies \tt{ 1^{2} + x^{2} = 3^{2}}$

⠀⠀⠀⠀⠀$:\implies \tt{ 1 + x^{2} = 9}$

⠀⠀⠀⠀⠀$:\implies \tt{  x^{2} = 9-1}$

⠀⠀⠀⠀⠀$:\implies \tt{  x^{2} = 8}$

⠀⠀⠀⠀⠀$:\implies \tt{  x = \sqrt{8}}$

⠀⠀⠀⠀⠀$\underline {\boxed{\pink{ \mathrm {  x = 2\sqrt {2}\: cm}}}}\:\bf{\bigstar}$

Therefore,

⠀⠀⠀⠀⠀$\underline {\therefore\:{ \mathrm {  Base  \:of\:Right \:Angled \:triangle \:is\:2\sqrt {2}\: cm}}}$

❒ Finding value of cot A by using found values :

$\sf{\underline {\dag As, \:We \:Know\:that \::}}$

• $\sf{\cot A =  \dfrac{Base} { Perpendicular} }$

Where ,

• Base of Right Angled Triangle is $2\sqrt {2}$.

• Perpendicular of Right angled triangle is 1 cm .

Therefore,

⠀⠀⠀⠀⠀$\sf{\cot A = \dfrac{2\sqrt{2}}{1}\:or\:2\sqrt{2}= \dfrac{Base} { Perpendicular} }$

$\underline {\boxed{\pink{ \mathrm { Hence,\:The\:Value \:of\:\cot A  = \dfrac{2\sqrt{2}}{1}\:or\:2\sqrt {2}\: }}}}\:\bf{\bigstar}$

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