Question

Hi, can you help me to solve this exercise, please!!

Answer 1

Based on the statement, we can deduce that cot(θ) must be negative as θ is in the fourth quadrant.

We have to find the ratio between the adjacent leg and the opposite leg knowing that the ratio between the hypotenuse and the opposite leg is -(√638)/22.

Using the pythagorean theorem for this purpose, we have:

`\begin{gathered} 638=484+a^2\text{ (Raising the numbers to the power of 2)} \\ 154=a^2(\text{ Subtracting 484 from both sides of the equation)} \\ \sqrt[]{154}=a\text{ (Taking the square root of both sides)} \end{gathered}`

`\begin{gathered} \text{ The ratio between the adjacent leg and the opposite leg would be: } \\ \frac{\sqrt[]{154}}{22} \end{gathered}`

Given that cot(θ) must be negative the answer would be:

`\cot \mleft(\theta\mright)=-\frac{\sqrt[]{154}}{22}`