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?

The Answer on Edge is C. 5/4

Answer 1

Answer: 5/4

Explanation:

Answer 2

`\sec \theta=(5)/(4).`

Explanation:

Use the definition of secans:

`\sec \theta=(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=\frac{\text{adjacent leg}}{\text{hypotenuse}}=(12)/(15)=(4)/(5)`

and

`\sec \theta=(1)/((4)/(5))=(5)/(4).`