Math, asked by kourharmanpreet980, 5 months ago

if 4 tan A= 3 then find Sin A and Cos A​

Answers

Answered by MoodyCloud
7

To find:-

  • Value of sin A and cos A.

Solution:-

Given that,

If 4 tan A = 3

Then tan A = 3/4

 \boxed{ \star \sf \:  tan  \: \theta =  \cfrac{Perpendicular}{Base} }

 \longrightarrow \sf \: tan  \: A =  \cfrac{3}{4}

 \boxed{ \star \sf \:  sin \:  \theta =  \cfrac{Perpendicular}{Hypothenuse} }

  • We don't have Hypothenuse.So,

According to Pythagoras theorem:

  \star \sf {Hypotenuse}^{2}  =  {Perpendicular}^{2} + {Base}^{2}

Perpendicular = 3

Base = 4

Put the values

 \implies \sf  {Hypotenuse}^{2}  =  {(3)}^{2}  +  {(4)}^{2}

 \implies  \sf  {Hypotenuse}^{2}  = 9 + 16

 \implies \sf  {Hypotenuse}^{2} = 25

 \implies \sf  Hypotenuse  =   \sqrt{25}

 \implies \sf \bold{ Hypotenuse  = 5}

So,

  \large\boxed{ \sf sin \:A =  \dfrac{3}{5}  }

And ,

 \boxed{ \star \sf \: cos  \: \theta =  \frac{Base}{Hypotenuse} }

 \large \boxed{ \sf cos \:A =  \frac{4}{5}  }

___________________

More ratio's:

 \star \sf \: cosec   \: \theta =  \dfrac{Hypotenuse}{Perpendicular}

 \star \sf \: sec \:  \theta =  \dfrac{Hypotenuse}{Base}

 \star \sf  \: cot \:  \theta =  \cfrac{Base}{Perpendicular}

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