Question

Find cot theta if csc theta = sqrt17/4 and tan theta >0.​

Answer 1

Answer:

$tan \theta = 4$

Step-by-step explanation:

We know that

$cosec \theta = \frac{hypotenuse }{opposite }$

Given :

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

So 4 is the opposite side of theta.

$tan \theta = \frac{opposite}{adjacent}$

We use the Pythagorean theorem to find for the adjacent side.

$a = \sqrt{17 - 4^2} = \sqrt{17-16} = 1$

$Therefore, \ tan \theta = \frac{4}{1} = 4$