Question

If sin θ =8/9. Find cot θ.

Answer 1

Step-by-step explanation:

✧ $\underline{ \underline{ \large{ \tt{G\: I \: V \: E\: N}}} }:$

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

♨ $\underline{ \underline{ \large{ \tt{ T \: O \: \: F \: I\: N\: D}}}} :$

• $\large{ \tt{cot \: \theta}}$

♨ $\underline{ \underline{ \large{ \tt{S \: O \: L\: U \: T\: I\: O \: N}}}} :$

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

☪ $\boxed{ \bf{ {h}^{2} = {p}^{2} + {b}^{2} }}$

~Plug all the known values and then simplify!

⇾ $\large{ \bf{ {9}^{2} = {8}^{2} + {b}^{2} }}$

⇾ $\large{ \bf{81 = 64 + {b}^{2} }}$

⇾ $\large{ \bf{64 + {b}^{2} = 81}}$

⇾ $\large{ \bf{ {b}^{2} = 81 - 64}}$

⇾ $\large{ \bf{ {b}^{2} = 17}}$

⇾ $\large{ \bf{b = \sqrt{17}}}$

• Now , Find the value of cot θ

We know ;

⟿ $\large{ \bf{cot \theta = \frac{b}{p} = \boxed{ \bf{ \frac{ \sqrt{17} }{8}}}}}$

⤷ $\boxed{ \boxed{ \underline{ \large{ \tt{Our \: Final \: Answer : { \tt{ \frac{ \sqrt{17} }{8} }}}}}}}$

( Correct me if I'm wrong )

Hope I helped ! ♡

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