Linearising Cosine: Taking Roots of Equation

[Agrajag]

Homework Statement

Linearise the following equation I(theta) = (I₁ – I₂ ) cos (2theta) + I₂
where I₁ and I₂ are constants.

Homework Equations

I(theta) = (I₁ – I₂ ) cos (2theta) + I₂

The Attempt at a Solution

Not sure how to linearise the cos(2theta). Have tried trig identities, would the best option be to take roots of both sides of the equation?

 

[friendbobbiny]

Hi Agrajag, what do you mean by linearize? I usually understand "linearization" to mean: find the closest linear approximation to the given curve. This can be found by taking the derivative at a point to be the slope of a line that goes through that same point. This line is your linearization.

 

[Agrajag]

Hi Agrajag, what do you mean by linearize? I usually understand "linearization" to mean: find the closest linear approximation to the given curve. This can be found by taking the derivative at a point to be the slope of a line that goes through that same point. This line is your linearization.

Hi friendbobbiny, the final equation should be in the form y=mx+c where y is I(theta) and x is theta.

 

[friendbobbiny]

Hi friendbobbiny, the final equation should be in the form y=mx+c where y is I(theta) and x is theta.

In that case, my approach works! Have you read into finding a linearization by taking a derivative at some point of interest (or at any point of interest)?