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# What is the slope of the tangent line to g(x)=cos(x+pi) at x=pi

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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.

Nov 24, 2018

#1
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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)

Nov 24, 2018
#2
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$$g(x) = \cos(x+\pi)\\ \text{the slope of the tangent line at }x=\pi \text{ is just}\\ \left . \dfrac{d}{dx}g(x) \right|_{x=\pi} = \left . -\sin(x+\pi) \right|_{x=\pi} =\\ -\sin(\pi + \pi) = -\sin(2\pi) = 0$$

Another way you can do this is to do some trig simplification first

$$\cos(x+\pi) = \cos(x) \cos(\pi) - \sin(x) \sin(\pi) = -\cos(x)$$

$$\dfrac{d}{dx}(-\cos(x)) = \sin(x)\\ \sin(\pi) = 0$$

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Nov 24, 2018
#3
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Remember

cos (x + pi)  =  - cos x

derivative of  - cos = sin x        at x = pi     sin (pi) = 0

Nov 24, 2018