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If sin θ =8/9. Find cot θ.

Sagot :

TheAnimeGirl

Step-by-step explanation:

✧ [tex] \underline{ \underline{ \large{ \tt{G\: I \: V \: E\: N}}} }: [/tex]

  • [tex] \large{ \tt{sin \: \theta = \frac{8}{9}}} [/tex] Here , Perpendicular ( p ) = 8 & hypotenuse ( h ) = 9

♨ [tex] \underline{ \underline{ \large{ \tt{ T \: O \: \: F \: I\: N\: D}}}} : [/tex]

  • [tex] \large{ \tt{cot \: \theta}}[/tex]

♨ [tex] \underline{ \underline{ \large{ \tt{S \: O \: L\: U \: T\: I\: O \: N}}}} : [/tex]

  • First, Find the base ( b ) using Pythagoras theorem :

☪ [tex] \boxed{ \bf{ {h}^{2} = {p}^{2} + {b}^{2} }}[/tex]

~Plug all the known values and then simplify!

⇾ [tex] \large{ \bf{ {9}^{2} = {8}^{2} + {b}^{2} }}[/tex]

⇾ [tex] \large{ \bf{81 = 64 + {b}^{2} }}[/tex]

⇾ [tex] \large{ \bf{64 + {b}^{2} = 81}}[/tex]

⇾ [tex] \large{ \bf{ {b}^{2} = 81 - 64}}[/tex]

⇾ [tex] \large{ \bf{ {b}^{2} = 17}}[/tex]

⇾ [tex] \large{ \bf{b = \sqrt{17}}} [/tex]

  • Now , Find the value of cot θ

We know ;

⟿ [tex] \large{ \bf{cot \theta = \frac{b}{p} = \boxed{ \bf{ \frac{ \sqrt{17} }{8}}}}} [/tex]

⤷ [tex] \boxed{ \boxed{ \underline{ \large{ \tt{Our \: Final \: Answer : { \tt{ \frac{ \sqrt{17} }{8} }}}}}}}[/tex]

( Correct me if I'm wrong )

Hope I helped ! ♡

Have a wonderful day / night ! ツ

☄ Let me know if you have any questions regarding my answer !

[tex] \underline{ \underline{ \mathfrak{Carry \: On \: Learning}}}[/tex] !! ✎

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