# Thread: Word Problem - derivatives in trig functions

1. ## Word Problem - derivatives in trig functions

In a Calculus problem, I found the rate of change of F with respect to x, resulting in:

dF/dx = -(uW)(ucos(x) - sin(x)) / (usin(x) + cos(x))^2

where u and W are coefficients. The problem then asks me to find when the rate of change is equal to 0, and it seems to indicate that I should find the equation that x is equal to.

How would I go about figuring out what x is? And in general, when there is a trigonometric function and I need to find x, how would I pull that variable out of the equation?

Another question involving the problem: If W = 70 and u = .7, how would I draw the graph of F [F = uW / (usin(x) + cos(x))]as a function of x and use it to find the value of x for which dF/dx = 0?

I plugged in the equation [y = 49/(.7sin(X) + cos(x)]into my graphing calculator and got the function. There was a curve like x^2 with the minimum at 34.992, so I thought that would be where where the derivative would equal 0, since there would be a horizontal tangent line there. However, Webassign said x = 34.992 was wrong. What am I doing wrong? And other than using the graphing calculator, is there another way to find x?

Thanks.

2. Originally Posted by Maziana
In a Calculus problem, I found the rate of change of F with respect to x, resulting in:

dF/dx = -(uW)(ucos(x) - sin(x)) / (usin(x) + cos(x))^2

where u and W are coefficients. The problem then asks me to find when the rate of change is equal to 0, and it seems to indicate that I should find the equation that x is equal to.

How would I go about figuring out what x is? And in general, when there is a trigonometric function and I need to find x, how would I pull that variable out of the equation?

$\displaystyle \textcolor{red}{u\cos{x} - \sin{x} = 0}$

$\displaystyle \textcolor{red}{u = \tan{x}}$

$\displaystyle \textcolor{red}{x = \arctan{u}}$

Another question involving the problem: If W = 70 and u = .7, how would I draw the graph of F [F = uW / (usin(x) + cos(x))]as a function of x and use it to find the value of x for which dF/dx = 0?

use a calculator

I plugged in the equation [y = 49/(.7sin(X) + cos(x)]into my graphing calculator and got the function. There was a curve like x^2 with the minimum at 34.992, so I thought that would be where where the derivative would equal 0, since there would be a horizontal tangent line there. However, Webassign said x = 34.992 was wrong. What am I doing wrong? And other than using the graphing calculator, is there another way to find x?

... x = 34.992 is correct. maybe a significant figure error? or maybe your original function for F is in error?

Thanks.
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