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July 15

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Trig function derivative (degrees)

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I think I asked this question a few years ago:

What is the derivative of while is in degrees? יהודה שמחה ולדמן (talk) 20:51, 15 July 2017 (UTC)[reply]

It is the derivative of the function with the argument expressed in radians multiplied by . Ruslik_Zero 20:56, 15 July 2017 (UTC)[reply]
 ? יהודה שמחה ולדמן (talk) 21:37, 15 July 2017 (UTC)[reply]
This is an easy consequence of the chain rule. Let and calculate .--Jasper Deng (talk) 04:09, 16 July 2017 (UTC)[reply]
  • But if you want the result to also be in degrees, don't you have to multiply this result by ? Then the result is just the unadjusted formula. Loraof (talk) 15:25, 16 July 2017 (UTC)[reply]
The function he has is dimensionless, so the units of the derivative should be inverse degrees, which agrees with the expression given above.--Jasper Deng (talk) 17:41, 16 July 2017 (UTC)[reply]
Actually the OP's function is the arctan function ("the angle whose tangent is ..."), whose dimensions are degrees or radians. Loraof (talk) 19:17, 16 July 2017 (UTC)[reply]
Right, I got the order of functions reversed. The conversion factor you mentioned should be applied at the beginning; then it drops out as you mentioned.--Jasper Deng (talk) 19:52, 16 July 2017 (UTC)[reply]