Finding the Slope of Tangent Line for Polar Curves

In summary, the conversation is about calculating a function of theta that gives the slope of the tangent line to a polar curve at a specific angle. The formula for dy/dx is provided, but the question is unclear. It is suggested to use the x= r cos theta, y= r sin theta, and dy/dx= dy/dtheta / dx/dtheta formulas to prove the formula.
  • #1
Justabeginner
309
1

Homework Statement


Calculate a function of theta that gives the slope of the tangent line (dy/dx) to the polar curve r at some angle theta.


Homework Equations


dy/dx= f'(theta)sin(theta) + f(theta)cos(theta)/[f'(theta)cos(theta) - f(theta) sin(theta)]


The Attempt at a Solution


I am not even understanding what the question is asking. All I know is the formula above. Can someone please help me out? Thank you.
 
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  • #2
That formula is the answer unless you are given some particular equation for the curve.
 
  • #3
Oh, okay. So they are just asking for me to prove how I got to that using the x= r cos theta, y= r sin theta, and dy/dx= dy/dtheta / dx/dtheta formulas. Thank you!
 

Related to Finding the Slope of Tangent Line for Polar Curves

1. What is the slope of tangent line-theta?

The slope of tangent line-theta refers to the slope of a curve at a particular point, which is represented by the Greek letter theta. It measures the steepness of the curve at that point and can be found by calculating the derivative of the function at that point.

2. How is the slope of tangent line-theta calculated?

The slope of tangent line-theta is calculated by taking the derivative of the function at the given point. This can be done using various methods, such as the power rule, product rule, or chain rule, depending on the complexity of the function.

3. What does the slope of tangent line-theta tell us about a curve?

The slope of tangent line-theta tells us the rate of change of the function at a specific point. It indicates how steep or flat the curve is at that point, and can also provide information about the direction of the curve.

4. How is the slope of tangent line-theta used in real-world applications?

The slope of tangent line-theta is used in various real-world applications, such as in physics, engineering, and economics. It can help in determining the velocity of an object, the rate of change of a physical system, or the marginal cost of a product.

5. Can the slope of tangent line-theta be negative?

Yes, the slope of tangent line-theta can be negative. This indicates that the curve is decreasing at that point, or that the function is decreasing in that direction. A positive slope indicates that the curve is increasing at that point, or that the function is increasing in that direction.

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