Question

Find cot θ if csc θ = square root of seventeen divided by four and tan θ > 0.

Answer 1

Answer:

$cot\theta=\frac{1}{4}$

Step-by-step explanation:

We have csc θ = square root of seventeen divided by four and tan θ > 0..

$cosec\theta =\frac{\sqrt{17}}{4}$

Now we need to find value of cot θ.

We have the expression

    $cosec^2\theta -cot^2\theta=1\\\\\left (\frac{\sqrt{17}}{4} \right )^2 -cot^2\theta=1\\\\cot^2\theta =\frac{17}{16}-1=\frac{1}{16}\\\\cot\theta =\pm \frac{1}{4}\\\\\texttt{Since }tan\theta >0\texttt{ we have }cot\theta >0\\\\cot\theta=\frac{1}{4}$

$cot\theta=\frac{1}{4}$

Answer 2

Hello! 
a = √17 - 4^2
a = 1

Cotangent theta is the adjacent over opposite. I used the Pythagorean Theorem to fine the adjacent side. The cotangent of theta is equal to 1/4.
I hope this helps :)