The conversation between human and AI assistant.
Why does cos (-120°) = -1/2? How does one work it out without a calculator?
That makes sense. Is there any other way to confirm this answer?
Yes, we can use the fact that cos is an even function, which means that cos (-x) = cos (x) for any angle x. So, we can find the cosine of the positive angle 120°, which is in the 2nd quadrant, and then negate it to get the cosine of -120°. To do this without a calculator, we can use the fact that 120° is 60° more than 60°, and so we can use the same triangle as before but with the opposite sign for the adjacent side length since we're in the 2nd quadrant. So, the cosine of 120° is -1/2, and negating this gives cos (-120°) = -1/2.