Answer: [tex]sin(360\°-\theta)=-sin\theta[/tex] is TRUE (See the explanation)
Step-by-step explanation:
To verify [tex]sin(360\°-\theta)=-sin\theta[/tex] you need to use the following identity:
[tex]sin(x\±y)=sin(x)\ cos(y)\±cos(x)\ sin(y)[/tex]
It is important to know that:
[tex]sin(360\°)=0\\\\cos(360\°)=1[/tex]
Then, knowing this, you get:
[tex]sin(360\°-\theta)=sin(360\°)\ cos\theta-cos(360\°)\ sin\theta=0\ cos\theta-1\ sin\theta=-sin\theta[/tex]
Therefore [tex]sin(360\°-\theta)=-sin\theta[/tex] is TRUE.
