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