Find the exact value of cot theta

Question

Given that $\theta$ is an acute angle with

$\sin (\theta)=\frac{17}{41}.$

find the exact value of $\cot (\theta)$

Answer 1

$$\cot \theta=\frac{\cos \theta}{\sin\theta}=\frac{\frac{4\sqrt{87}}{41}}{\frac{17}{41}}=\frac{4\sqrt{87}}{17}$$

Answer 2

Hint: $\cos^2\theta+\sin^2\theta=1$ . Use this to get $\cos\theta$.

Then $\cot\theta =\frac{\cos\theta}{\sin\theta}$...

Answer 3

$$sin \theta=17/41 \implies $$

$$ cos \theta = \sqrt {1-sin^2 \theta }= 4\sqrt {87}/41\implies $$

$$cot\theta = \frac {cos \theta}{sin \theta} = 4\sqrt {87}/17 $$