Answer:
[tex]cot\theta =\frac{\sqrt{17}}{8} [/tex]
Step-by-step explanation:
We have
[tex]sin\theta =\frac{8}{9}[/tex]
We know that
[tex]cot\theta =\frac{cos\theta}{sin\theta} [/tex]
[tex]cos\theta =\sqrt{1-sin^2\theta}=\sqrt{1-\left (\frac{8}{9} \right )^2}=\sqrt{1-\frac{64}{81}}=\frac{\sqrt{17}}{9} [/tex]
Substituting
[tex]cot\theta =\frac{\frac{\sqrt{17}}{9}}{\frac{8}{9}}=\frac{\sqrt{17}}{8} [/tex]
