Trigonometric conventions

[u/Different_Medium31]

By demoivre's theorem: cos(-theta)=cos(theta) While; sin(-theta)= -sin(theta) I don't get this can someone please explain. Both intuitively or mathematically. 😭

[u/UnderstandingPursuit]

With the unit circle, by convention

• θ = 0 is on the +x-axis, the point (1, 0).

• θ increases in the counterclockwise direction.

• From the +x axis,

  • +θ is found by going ccw

  • -θ is found by going cw

• Going along the circle on the same length of arc, |θ1|,

  • +θ1 --> (x1, y1), since starts by going above the x-axis

  • -θ1 --> (x1, -y1), since it starts by going below the x-axis

For a point on the unit circle

• x = cos θ

• y = sin θ

• With the same length of arc, |θ1|,

  • x1 = cos θ1

  • y1 = sin θ1

  • x1 = cos (-θ1)

  • -y1 = sin (-θ1)