1 answer
(click or scroll down)
To evaluate each of these expressions using the unit circle, we need to find the exact values of sine and cosine for the corresponding angles.
a. sin 150° cos(−300°) − sin 810° cos 240°
sin 150° = sin(180° - 30°) = sin 30° = 0.5
cos(-300°) = cos(360° - 300°) = cos 60° = 0.5
sin 810° = sin(720° + 90°) = sin 90° = 1
cos 240° = cos(180° + 60°) = -cos 60° = -0.5
Therefore, the expression becomes:
0.5 * 0.5 - 1 * (-0.5)
= 0.25 + 0.5
= 0.75
So, sin 150° cos(−300°) − sin 810° cos 240° = 0.75.