Question

find sinƟ, if cosƟ = 3/5​

Answer 1

Answer:

See the picture for your answer

Answer 2

Given: $cos \theta = \dfrac{3}{5}$

Exigency to find : $sin \theta$

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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,

• $\sf{\cos \theta = \dfrac{3}{5}= \dfrac{Base} { Hypotenuse} }$

Therefore,

• Base of Right Angled Triangle is 3 .

• Hypotenuse of Right angled triangle is 5 .

⠀⠀⠀⠀⠀Finding Perpendicular of Right angled triangle :

❍ Let's Consider Perpendicular of Right Angled Triangle be x .

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

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

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

⠀⠀⠀⠀⠀$:\implies \tt{ 3^{2} + x^{2} = 5^{2}}$

⠀⠀⠀⠀⠀$:\implies \tt{ 9 + x^{2} = 25}$

⠀⠀⠀⠀⠀$:\implies \tt{  x^{2} = 25- 9}$

⠀⠀⠀⠀⠀$:\implies \tt{  x^{2} = 16}$

⠀⠀⠀⠀⠀$:\implies \tt{  x = \sqrt{16}}$

⠀⠀⠀⠀⠀$\underline {\boxed{\pink{ \mathrm {  x = 4\: cm}}}}\:\bf{\bigstar}$

Therefore,

⠀⠀⠀⠀⠀$\underline {\therefore\:{ \mathrm {  Perpendicular   \:of\:Right \:Angled \:triangle \:is\:\bf{4\: }}}}$

❒ Finding value of sin $\theta$ by using found values :

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

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

Where ,

• Perpendicular of Right Angled Triangle is 4 .

• Hypotenuse of Right angled triangle is 5 .

Therefore,

⠀⠀⠀⠀⠀$\sf{\sin \theta = \dfrac{4}{5}= \dfrac{Perpendicular} { Hypotenuse} }$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {\:Hence,\:The\:Value \:of\:\sin \theta  = \:\:\bf{\dfrac{4}{5}}}}}$

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