Question

An angle measures 120 degrees. Describe how to use special right triangles and the unit circle as tools to calculate the sine and cosine of this angle.

Answer 1

We know that, for a right triangle:

Cos(A) = (adjacent cathetus)/hipotenuse

sin(A) = (opposite cathetus)/Hipotenuse.

If we are in a right triangle inside the unit circle, we have that hypotenuse = 1.

Now, when you draw the unit circle, now from the center of the axis you must draw a straigth line (that forms an angle of 120° with the x-axis), and in the point where it cuts the unit circle we do 2 things.

from this point, you can draw a parallel line to the y-axis, the point where this line touches the x-axis is the value of the cosine.

Now you draw a line that is parallel to the x-axis (remember that the line must pass trough the point of before), the point where this line cuts the y-axis is the value of the sine

You should get:

sin(120°) = 0.87

cos(120°) = -0.5