Question

derivative of cos(5-theta)

Answer 1

use chain rule

Answer 2

so would my answer be sin(theta-5) ??

Answer 3

not quite...why did you reverse the (5 - theta)

Answer 4

becuase...
cos(5-theta)
(d/dx)=-sin(5-theta)(-1)
(d/dx)=sin(theta-5)

Answer 5

That's valid since \(\sin x\) is an odd function; i.e. \(\sin (-x)=-\sin x\). What @gymkara did was reverse this property by noting that \(-\sin(5-\theta) = \sin(-(5-\theta)) = \sin(\theta-5)\).

Answer 6

however, there's still a negative sign missing in his derivative!

Answer 7

exactly!

Answer 8

I just realized that... >_>

Answer 9

so should it be
-sin(theta-5) ?

Answer 10

You didn't apply chain rule!

\((\cos(5-\theta))^{\prime} = -\sin(5-\theta)\cdot{\color{red}{(5-\theta)^{\prime}}} =\ldots\)

Answer 11

I don't use identities unless I need to so my answer would have been:
-sin(5-theta)*-1 = sin(5 - theta)

Answer 12

@ChristopherToni if I take the derivative of the part in red, it's -1...so if I multiply -sin(5-theta) by -1, I get sin(theta-5)

Answer 13

\(-\sin(5-\theta) \cdot (-1) = \sin(5-\theta)\), not \(-\sin(5-\theta)\).

Answer 14

Oh DUH!!! I'm stupid!! Thank you :)

Answer 15

No worries; at least you see where you were going wrong - that's the important part! :-)