Question

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

For the point (16, 12), find sintheta and costheta.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the trigonometric functions for the standard-position angle determined by the point (x, y) = (16, 12), we first need to find the value of r, which is the distance from the origin to the point (x, y). We can use the Pythagorean theorem to find r:

r = √(x^2 + y^2)
r = √(16^2 + 12^2)
r = √(256 + 144)
r = √400
r = 20

Now, we can find the values of sine and cosine:

sinθ = y/r
sinθ = 12/20
sinθ = 0.6

cosθ = x/r
cosθ = 16/20
cosθ = 0.8

Therefore, sinθ = 0.6 and cosθ = 0.8 for the standard-position angle determined by the point (16, 12).