For a standard-position angle determined by the point (x, y), what are the values of the trigonometric functions?

For the point (6, 8), find csc θ and sec θ.'

A. csc θ = 5/4, sec θ = 4/5

B. csc θ = 5/4, sec θ = 5/3

C. csc θ = 4/5, sec θ = 5/3

D. csc θ = 4/5, sec θ = 3/5

1 answer

We can use the Pythagorean theorem to find the length of the hypotenuse:

h = sqrt(x^2 + y^2) = sqrt(6^2 + 8^2) = 10

Then, we can use the definitions of the trigonometric functions:

sin θ = y/h = 8/10 = 4/5
cos θ = x/h = 6/10 = 3/5
tan θ = y/x = 8/6 = 4/3
csc θ = 1/sin θ = 5/4
sec θ = 1/cos θ = 5/3

Therefore, the answer is B. csc θ = 5/4, sec θ = 5/3.