agentnerdo said:Homework Statement
differentiate F=Fi (sin ct)
The Attempt at a Solution
Fi is a constant
= Fi (-cos ct)(c)
That is the solution I keep getting, but my buddy keeps getting
Fi (- cost ct)/c
in other words, he thinks - cost ct should be divided by c, anyone care to shed some light?
thanks in advance!
╔(σ_σ)╝ said:lol. I think you need to fix your post.
Your final formula is not correct.
Inferior89 said:Wuups... It is 4:30 AM where I live :( ...
In this equation, F represents a function, Fi represents a constant, sin represents the sine function, and ct represents the product of the speed of light and time. This equation is commonly used in physics to describe the behavior of electromagnetic waves.
To differentiate this equation, you can use the chain rule. First, take the derivative of the outer function, which is F, with respect to the inner function, sin(ct). This will result in Fi multiplied by the derivative of sin(ct) which is cos(ct). Then, multiply by the derivative of the inner function, which is c. Therefore, the final derivative is F'= Fi*c*cos(ct).
Yes, this equation can be simplified by using trigonometric identities. For example, sin(ct) can be written as (1/2)(e^(ict)-e^(-ict)), where i is the imaginary unit. This simplification can be useful in certain applications.
The constant Fi is typically measured in units of electric field strength, while the product of the speed of light and time (ct) is measured in units of distance.
This equation is significant in physics because it represents the mathematical relationship between electromagnetic waves, which are fundamental to many aspects of our daily lives including communication, technology, and energy. It also helps to explain the properties and behavior of light and other electromagnetic radiation.