Answer:
[tex]cot\theta=\frac{\sqrt{13}}{6}[/tex]
Step-by-step explanation:
Step 1
Find the value of the [tex]cos\theta[/tex]
we have that
[tex]sin\theta=\frac{6}{7}[/tex]
Remember that
[tex]sin^{2} \theta+cos^{2} \theta=1[/tex]
Substitute the value of [tex]sin\theta[/tex]
[tex]\frac{6}{7}^{2}+cos^{2} \theta=1[/tex]
[tex]\frac{36}{49}+cos^{2} \theta=1[/tex]
[tex]cos^{2} \theta=1-\frac{36}{49}[/tex]
[tex]cos^{2} \theta=\frac{13}{49}[/tex]
square root both sides
[tex]cos \theta=\frac{\sqrt{13}}{7}[/tex]
Step 2
Find the value of [tex]cot\theta[/tex]
we know that
[tex]cot\theta=\frac{cos\theta}{sin\theta}[/tex]
substitute the values
[tex]cot\theta=\frac{\frac{\sqrt{13}}{7}}{\frac{6}{7}}=\frac{\sqrt{13}}{6}[/tex]
