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# Derivative

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So I was given the equation f(t)= cos(pi(t) / 6) and was told to find the velocity equation which was the first derivative,

V(t)= -(pi/6) [sin(pi(t)/6)].  The part I'm having trouble with is finding the velocity after 1 second. I plugged in 1 into the velocity equation and got an answer but it keeps saying it's wrong and I have no idea what I'm doing wrong.

Mar 9, 2019

#1
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$$f(t) = \cos\left(\dfrac{\pi t}{6}\right)\\ \dfrac{df}{dt}(t) = -\sin\left(\dfrac{\pi t}{6}\right)\cdot \dfrac \pi 6\\ \dfrac{df}{dt}(1) = -\sin\left(\dfrac{\pi}{6}\right)\cdot \dfrac \pi 6 = -\dfrac 1 2 \dfrac \pi 6 = -\dfrac{\pi}{12}$$

What did you get?

Mar 9, 2019
#2
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My calculator kept giving me -0.004784853  but it's probably just because I was putting it in wrong.  Thank you.

Ruublrr  Mar 9, 2019
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check that you've got it set to use whatever units you are, radians or degrees

Rom  Mar 9, 2019
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I just realized my calculator was in degree mode so I'm pretty sure that is the reason I was getting the wrong answer

Ruublrr  Mar 9, 2019