Question

Suppose that is an angleand y is not in the first quadrant. Compute the exact value of secyYou do not have to rationalize the denominator. with * cot gamma = 9/13

Answer 1

ANSWER :

The answer is :

$-\frac{5\sqrt{10}}{9}$

EXPLANATION :

Note that cotangent is only positive when the angle is in the first or third quadrant.

Since y is not in the first quadrant, it must be in the third quadrant.

So the x and y are both negative.

An angle with a terminal point (x, y)

The cotangent is x/y

We can equate :

$\cot\gamma=\frac{9}{13}=\frac{x}{y}$

Since x and y are both negatives, x = -9 and y = -13

We can have the triangle :

The hypotenuse will be :

$\begin{gathered} c=\sqrt{(-9)^2+(-13)^2} \\ c=5\sqrt{10} \end{gathered}$

We are asked to find the value of sec y.

In an angle with a terminal point (x, y)

The secant is :

$\sec\gamma=\frac{\text{ hypotenuse}}{x}$

The hypotenuse is 5√10 and x = -9

The value of sec will be :

$\begin{gathered} \sec\gamma=\frac{5\sqrt{10}}{-9} \\ \\ =-\frac{5\sqrt{10}}{9} \end{gathered}$