Differentiating a tricky trig function

[JACKTHEHAT]

Hi everybody,
This is my first post and I hope someone can help.
It's been 40 years since I did maths in a serious way. I have knowledge maths to first year university level as I studied Physics and Astronomy at university in the 1970's, but I am very rusty in all of these subjects and maths in particular. I am starting to take up Physics again and I have come across and example that requires me to find the derivative of an function which contains trigonometric expressions and I am uncertain as to how to solve it.

The function is ... F = a.b/(cos c - d. sin c) , where a,b d are constants and c is an angle.

I have to take the derivative dF/dc (that is derivative of F with respect to the angle c).

Can anybody show me how to go about this ... remember I haven't used calculus for about 40 years ... so I am a bit hazy on detail;s.
Thanks.
JacktheHat

 

[stapel]

The function is ... F = a.b/(cos c - d. sin c) , where a,b d are constants and c is an angle.

I have to take the derivative dF/dc (that is derivative of F with respect to the angle c).

Can anybody show me how to go about this ... remember I haven't used calculus for about 40 years ... so I am a bit hazy on detail;s.

While we cannot provide weeks ("years"?) of classroom instruction within this environment, we'll be glad to try to find lesson links so you can do the study necessary to refresh on the background material. To get us started, please clarify the "details" on which you are "a bit hazy". Do you remember anything about differential calculus? Do you remember anything about trigonometry and the basic identities?

Note: Your school was supposed to have tested you to determine your current mathematical knowledge, precisely so that you would not find yourself in this exact situation of having to try to re-learn a few years of math classes on your own. Shame on them!

 

[JACKTHEHAT]

Hi thanks for replying,
I know the basic rules of differentiation and integration and also the basics of trigonometry. However the function I have to differentiate ... F= a.b/(cos c - d. sin c) is not as straightforward to differentiate to me, as it probably looks to you.
I know that the differential of cos = -sin and sin = cos when differentiated. However I am unsure of other parts of the function. Namely, I'm not sure if I should treat this function as it appears above or would it be better to look at it in the form .. F = (a.b)(cos c - d. sin c) to the power -1 .. in order to differentiate.
Also the numerator being the product of two constants .. after differentiation does the numerator become equal to zero ? .. if so what does that leave me with as a result of the differentiation.
This function originally comes from a Physics (Dynamics) problem where F is a force being applied to a mass at an angle in order to move the mass. The problem is to find a value for the angle for the specific minimum value of F required to move the mass at a constant speed (ie. acceleration = 0). So I have to find the minimum value of the function (ie. dF/dc = 0).
Does this make sense ... does it help ?
Regards,
JacktheHat

 

[stapel]

I know the basic rules of differentiation and integration and also the basics of trigonometry. However the function I have to differentiate ... F= a.b/(cos c - d. sin c) is not as straightforward to differentiate to me....

Okay; excellent! Now:

Would you be able to differentiate something like the following?

. . . . .\(\displaystyle F(x)\, =\, \dfrac{3\,\times\, 5}{\cos(x)\, -\, 4\sin(x)}\)

You'd start by multiplying together the numerator, but... then what?

Note: If you can do the above, then you can do the one you posted. The only difference is that you can't simplify as much, because you don't have values for the constants. But those constants are only numbers! (Oh, and they're using "c" instead of "x". But everything else is just the same.)

 

[Deleted member 4993]

Hi everybody,
This is my first post and I hope someone can help.
It's been 40 years since I did maths in a serious way. I have knowledge maths to first year university level as I studied Physics and Astronomy at university in the 1970's, but I am very rusty in all of these subjects and maths in particular. I am starting to take up Physics again and I have come across and example that requires me to find the derivative of an function which contains trigonometric expressions and I am uncertain as to how to solve it.

The function is ... F = a.b/(cos c - d. sin c) , where a,b d are constants and c is an angle.

I have to take the derivative dF/dc (that is derivative of F with respect to the angle c).

Can anybody show me how to go about this ... remember I haven't used calculus for about 40 years ... so I am a bit hazy on detail;s.
Thanks.
JacktheHat

Can you differentiate 1/x?

Can you differentiate cos(x) - d*sin(x)?

Do you remember chain rule?