Question

Find sec Θ if the terminal side of Θ in standard position contains the point (4, -3)?

a. -3/4

b. -5/3

c. 5/4

d. 4/5

Answer 1

If we plot the point (4, -3), we find ourselves in QIV. Drawing a line to connect the origin to the point creates a right triangle with a base of 4 and a height of -3. We need to find the length of the hypotenuse. Using Pythagorean's Theorem,
`4^2+-3^2=c^2` and
`16+9=c^2`. So c = 5. The secant identity is the coidentity of cosine, and cosine's ratio is side adjacent over hypotenuse; that means that the secant ratio is hypotenuse over side adjacent. That ratio for secant is 5/4, choice c from above.