Question

Assume that (θ) is an angle in standard position whose terminal side contains the point (-12,5). Find the exact values of the following functions.

sin(θ)
cos(θ)
etc.

Answer 1

To find the exact values of sin(θ) and cos(θ), we use the right triangle formed by the given point (-12,5) which is in standard position. Using the Pythagorean theorem, we find that r = 13. Using the values of Ay and Ax, we can finally compute sin(θ) and cos(θ) as 5/13 and -12/13, respectively.

Step-by-step explanation:

In this problem, we are given that the angle (θ) is in standard position and its terminal side contains the point (-12,5). To find the exact values of sin(θ) and cos(θ), we can use the right triangle formed by the x-coordinate (-12), y-coordinate (5), and the hypotenuse (r) which can be found using the Pythagorean theorem. From this triangle, we can determine that sin(θ) = Ay/r and cos(θ) = Ax/r. Considering the given point, we have Ay = 5 and Ax = -12. So, we need to find the value of r to compute sin(θ) and cos(θ).

Using the Pythagorean theorem, we can find r as follows: r = sqrt(Ax^2 + Ay^2) = sqrt((-12)^2 + 5^2) = sqrt(144 + 25) = sqrt(169) = 13.

Now that we have r = 13, we can calculate sin(θ) and cos(θ) as follows: sin(θ) = Ay/r = 5/13 and cos(θ) = Ax/r = -12/13.