Is $\sin(x)$ =$-\sin(180^o+x)$?

Question

I figured out that $\sin(x)$ should equal $-\sin(180+x)$ like in this picture

But when I type on Wolfram $$\sin(a\mathrm{deg})=-\sin(180+a \mathrm{deg})$$ it says it's false. Why? I've tested it using my calculator and it's right. Is this formula wrong?

Answer 1

We know: sin(A+B)=sin A cos B + cos A sin B

And therefore: sin(180 + x) = -sin (x)

And in end we have: sin(x) = -sin(180 + x)

Answer 2

When I entered "sin(x deg) = -sin(180 deg + x deg)" into WA, I got the response "True." Note I specified "180 deg" and not just "180 + x deg." I also put spacing in "x deg" (not just "xdeg"). I'm not sure what WA requires, but some experimentation should provide clues.

Answer 3

According to my calculations,the answer is yes. sin(45) is the same as -sin 225 (180+45)=.7071. Hope this helps.