Radian vs. Degree, Sin DerivativesDate: 10/23/2001 at 23:51:41 From: Liz Subject: Radian and degree, sin derivatives Dr. Math, Why do you get two different answers when you ask your calculator for the derivative of sinx in degree and radian modes? When you have it in radian mode, it gives you the right answer (the cosx). When you put it in degree mode, it gives you pi*cosx/180. Why is that? Liz Date: 10/24/2001 at 17:02:57 From: Doctor Peterson Subject: Re: Radian and degree, sin derivatives Hi, Liz. In degree mode, the calculator is essentially replacing the sine function with a different function whose argument is a number of degrees. If we call this new function sind, we can define it as sind(x) = sin(pi/180 x) since to calculate it we have to convert x degrees to radians and then take the actual sine. Take the derivative of this with respect to x, and you get d/dx sind(x) = pi/180 cos(pi/180 x) = pi/180 cosd(x) Of course, what the calculator calls the cosine is now really this "cosd" function. Does that help? This also explains why we use radians when we do calculus. Like many things mathematicians do, this makes everything easier. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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