Question

sin tita 1/2 then the value of cos tita​

Answer 1

Given : $\sf{\sin \theta = \dfrac{1}{2}}$

Need To Find : The value of $\cos \theta$ .

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❍ Basic Formulas of Trigonometry is given by :

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

Then,

• $\sf{\sin \theta = \dfrac{1}{2}= \dfrac{Perpendicular} { Hypotenuse} }$

Therefore,

• Perpendicular of Right Angled Triangle is 1 cm .

• Hypotenuse of Right angled triangle is 2 cm .

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

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

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

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

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

⠀⠀⠀⠀⠀$:\implies \tt{ 1 + x^{2} = 4 }$

⠀⠀⠀⠀⠀$:\implies \tt{  x^{2} = 4 - 1}$

⠀⠀⠀⠀⠀$:\implies \tt{  x^{2} = 3}$

⠀⠀⠀⠀⠀$:\implies \tt{  x = \sqrt{3}}$

⠀⠀⠀⠀⠀$\underline {\boxed{\pink{ \mathrm {  x = \sqrt{3}\: cm}}}}\:\bf{\bigstar}$

Therefore,

⠀⠀⠀⠀⠀$\underline {\therefore\:{ \mathrm {  Base  \:of\:Right \:Angled \:triangle \:is\:\sqrt {3}\: }}}$

❒ Finding value of $\bf{\cos\theta}$ by using found values :

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

$\sf{\cos \theta =  \dfrac{Base} { Hypotenuse} }$

Where ,

• Base of Right Angled Triangle is $\sqrt {3}$.

• Hypotenuse of Right angled triangle is 2 .

Therefore,

⠀⠀⠀⠀⠀$\sf{\cos \theta = \dfrac{\sqrt{3}}{2}= \dfrac{Base} { Hypotenuse} }$

$\underline {\boxed{\pink{ \mathrm { Hence,\:The\:Value \:of\:\cos \theta  = \dfrac{\sqrt{3}}{2}\: }}}}\:\bf{\bigstar}$

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