What is the slope of the tangent line to g(x)=cos(x+pi) at x=pi
I've never been shown a question with pi before so I'm super confused.
+157 Wait, if you've never seen a question with pi in it before, you don't know how to find area or perimeter of a circle. Why did you get this question, then? (by the way, I don't know anything about tangents)
+6250 \(g(x) = \cos(x+\pi)\\ \text{the slope of the tangent line at }x=\pi \text{ is just}\\ \left . \dfrac{d}{dx}g(x) \right|_{x=\pi} = \left . -\sin(x+\pi) \right|_{x=\pi} =\\ -\sin(\pi + \pi) = -\sin(2\pi) = 0\)
Another way you can do this is to do some trig simplification first
\(\cos(x+\pi) = \cos(x) \cos(\pi) - \sin(x) \sin(\pi) = -\cos(x)\)
\(\dfrac{d}{dx}(-\cos(x)) = \sin(x)\\ \sin(\pi) = 0\)
+37155 Remember
cos (x + pi) = - cos x
derivative of - cos = sin x at x = pi sin (pi) = 0
