If a vertical line is dropped from the x-axis to the point (12, –9) in the diagram below, what is the value of sec?

Question

asked Feb 18, 2019 133k views

2 Answers

Jim Ma · Answer 1 · 2019-02-22T19:43:18+0000

Answer:

Value of
$\sec \theta = (5)/(4)$

Explanation:

Given: A vertical line is dropped from the x-axis to the point (12, -9) as shown in the diagram below;

To find the value of
$\sec \theta$ .

By definition of secants;

$\sec \theta = (1)/(\cos \theta)$

Now, first find the cosine of angle
$\theta$

As the point (12 , -9) lies in the IV quadrant , where
$\cos \theta > 0$

Consider a right angle triangle;

here, Adjacent side = 12 units and Opposite side = -9 units

Using Pythagoras theorem;

(Hypotenuse side)^2= (12)^2 + (-9)^2 = 144 + 81 = 225

or

Hypotenuse = √(225) =15 units

Cosine ratio is defined as in a right angle triangle, the ratio of adjacent side to hypotenuse side.

$\cos \theta = (Adjacent side)/(Hypotenuse side)$

then;

$\cos \theta = (12)/(15) = (4)/(5)$

and

$\sec \theta = (1)/(\cos \theta)= (1)/((4)/(5)) = (5)/(4)$

therefore, the value of
$\sec \theta$ is,