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

These relations all follow from the identity,

sin(x - y) = sin(x) cos(y) - cos(x) sin(y)

Notice that 160° = 180° - 20°, so if x = 180° and y = 20° above, we get

sin(160°) = sin(180°) cos(20°) - cos(180°) sin(20°)

We know sin(180°) = 0 and cos(180°) = -1, so we end up with

sin(160°) = sin(20°)

For the other, notice that 200° = 360° - 160°, and 340° = 360° - 20°.

answer: i guess 5 units?

step-by-step explanation: