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Why does cos (-120°) = -1/2? How does one work it out without a calculator?
Can you explain why cos (-120°) equals -1/2? And is it possible to work it out without a calculator?
Certainly! When you take the cosine of an angle, it's equal to the adjacent side length over the hypotenuse length in a right triangle that has that angle. In the case of -120°, we're dealing with a reference angle of 60°, which has an adjacent side length of 1 and a hypotenuse length of 2. Since the cosine of the angle is negative, we know that it must lie in the 2nd or 3rd quadrant. And since it's 120° from the x-axis, the x-coordinate of the point on the unit circle must be -1/2. So, cos (-120°) = -1/2.