Question

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

Answer 1

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 :)

Answer 2

`cot\theta=(1)/(4)`

Explanation:

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

`cosec\theta =(√(17))/(4)`

Now we need to find value of cot θ.

We have the expression

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

`cot\theta=(1)/(4)`