Question

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 theta?

Answer 1

Answer: 5/4

Step-by-step explanation:

Answer 2

Answer:

$\sec \theta=\dfrac{5}{4}.$

Step-by-step explanation:

Use the definition of secans:

$\sec \theta=\dfrac{1}{\cos \theta}.$

Now you have to find the cosine of angle $\theta.$

Point (12,-9) lies in fourth quadrant, then $\cos \theta>0.$

Consider right triangle with legs 9 and 12, by the Pythagorean theorem,

$\text{hypotenuse}^2=9^2+12^2=81+144=225,\\ \\\text{hypotenuse}=15.$

Thus,

$\cos \theta=\dfrac{\text{adjacent leg}}{\text{hypotenuse}}=\dfrac{12}{15}=\dfrac{4}{5}$

and

$\sec \theta=\dfrac{1}{\dfrac{4}{5}}=\dfrac{5}{4}.$