To find the exact value of cos(180) multiplied by sin(180), we start by calculating each trigonometric function individually.
The value of cos(180) is determined using the unit circle, where the angle 180 degrees corresponds to the point (-1, 0). Therefore:
cos(180) = -1
Next, we find sin(180). The angle 180 degrees also corresponds to the same point on the unit circle, where the y-coordinate is 0:
sin(180) = 0
Now that we have both values, we can multiply them together:
cos(180) * sin(180) = -1 * 0 = 0
Thus, the exact value of cos(180) * sin(180) is 0.