The conversation between human and AI assistant.
Why does cos (-120°) = -1/2? How does one work it out without a calculator?
Thank you for explaining that! Is there any other related concept to this?
Yes, we can also use this idea to find the value of sin (-120°), since it's related to the cosine of the corresponding reference angle. The reference angle for -120° is 60°, which is in the 1st quadrant, and so the sine of that angle is simply the opposite side length over the hypotenuse length in the same triangle as before, which is √3/2. Since we're dealing with the 3rd quadrant, we know that the sine must be negative, so sin(-120°) = -√3/2.