Question

For a standard-position angle determined by the point (x, y) what are the values of the trigonometric functions ? For the point (5, 12) , find csc(theta) and sec(theta)

Answer 1

[AI-generated answer — Bot GPT 3.5]

First, we need to find the values of sine, cosine, and tangent for the point (5, 12).

Let r be the distance from the point to the origin, which can be found using the Pythagorean theorem:
r = √(5^2 + 12^2)
r = √(25 + 144)
r = √169
r = 13

Now, we can find sine, cosine, and tangent:
sin(theta) = y/r = 12/13
cos(theta) = x/r = 5/13
tan(theta) = y/x = 12/5

Now, we can find the values of csc(theta) and sec(theta):
csc(theta) = 1/sin(theta) = 13/12
sec(theta) = 1/cos(theta) = 13/5

Therefore, csc(theta) = 13/12 and sec(theta) = 13/5 for the point (5, 12).