Question

Why is sin(20) = sin(160) = -sin(200) = -sin(340)?

Answer 1

u talking about the answer or the question ?

Answer 2

think about the unit circle. sin(theta) is the y-value for the given theta value. notice how for sin(20) and sin(160) these two angles are the same vertical distance from the x-axis, and thus have the same y value and thus the same sin value. Therefore, sin(20) = sin(160).

You can repeat this logic by drawing sin(200) and sin(340), noticing that they're the same distance from the x-axis, but in the opposite (negative) y-direction, thus -sin(200) and -sin(340) being equal to each other as well as equal to both sin(20) and sin(160).