Respuesta :
Answer:
A nice way to show it is through the unit circle.
In the unit circle, the point at angle theta from the origin has a y value of sin theta.
If you rotate a point 360-theta degrees from the origin, that is like rotating it theta degrees "backwards", or downwards, which is going to yield the same exact point, reflected through the x-axis. In other words, the y value, or sin(360-theta), is exactly -sin(theta).
Answer:
The verification is in the explanation.
Step-by-step explanation:
To solve this I'm going to use the difference identity for sine:
[tex]\sin(a-b)=\sin(a)\cos(b)-\sin(b)\cos(a)[/tex].
[tex]\sin(360^\circ-\theta)=\sin(360^\circ)\cos(\theta)-\sin(\theta)\cos(360^\circ)[/tex]
We are going to apply that [tex]\sin(360^\circ)=0 \text{ while } \cos(360^\circ)=1[/tex]
[tex]\sin(360^\circ-\theta)=0 \cdot \cos(\theta)-\sin(\theta)\cdot 1[/tex]
[tex]\sin(360^\circ-\theta)=-\sin(\theta)[/tex]
