Determine the exact values of sin? of the angle. (-8,-20)

Question

Assume the given point is on the terminal side of an angle in standard position. Determine the exact values of sinθ of the angle. (-8,-20)

Answer 1

Given the point (-8, -20), the terminal side of the angle (θ) is in the third quadrant, and the total angle in degrees is 180 + Φ, where Φ is the angle from the negative x-axis to the terminal side of θ.

 

Find Φ by using the x and y values given to form a right triangle with the hypotenuse being the terminal side of θ:

tan(Φ) = 20/8

Φ = tan^-1(20/8) = 68.2°

 

θ = 180 + Φ = 248.2°