Equation of a Tangent Line to a Polar Curve

In summary, the conversation discussed finding the equation of the tangent line to the curve x=t4+1, y=t3+t when t=-1. The slope of the tangent line was found to be -1 by calculating the derivative and the next step was to find a point on the tangent line. It was suggested to set the equations equal to each other and solve, but the specific point of intersection was not known. The conversation ended with the suggestion to consider the point at which t equals negative one as the tangent line point.
  • #1
zmilot
4
0
I need to find the equation of the tangent line to the curve

x=t4+1, y=t3+t; t=-1

I have already found that the slope of the line is -1 by finding (dy/dt)/(dx/dt) I just need to figure out how to solve for y1 and x1

Thanks in advance
 
Physics news on Phys.org
  • #2
Hi zmilot! :smile:

zmilot said:
I need to find the equation of the tangent line to the curve

x=t4+1, y=t3+t; t=-1

I have already found that the slope of the line is -1 by finding (dy/dt)/(dx/dt) I just need to figure out how to solve for y1 and x1

Thanks in advance

So you've got the slope of the tangent line, that's good. Can you find a point on the tangent line?? If you have the slope and any point, then you can easily find the equation with certain formulas.
 
  • #3
Thats what I was trying to figure out, how do you find a point on the tangent line, all I have is the slope and I don't know where they intersect
 
  • #4
zmilot said:
Thats what I was trying to figure out, how do you find a point on the tangent line, all I have is the slope and I don't know where they intersect

What's the intersection of the tangent line with the curve?
 
  • #5
The only way I know to find the intersection is to set the equations equal to each other, but since I don't have the tangent line equation I am not sure how to go about this.
 
  • #6
When t=-1, what is x? What is y? is this the point for which you calculated the derivative?
 
  • #7
I don't think they line intersects at t=-1, that was just the number we were given to plug into the first derivative in order to find the slope. I am really lost on this problem so if anyone could make sure my first step is right and then walk me through the rest of the process it would be greatly appreciated.
 
  • #8
You found the tangent line to the point at which t equals negative one. I wasn't really asking a question so much as inviting you to see it.
 
  • #9
You're taking the tangent line of the curve at t=-1. What does that mean?
 

Related to Equation of a Tangent Line to a Polar Curve

1. What is the equation of a tangent line to a polar curve?

The equation of a tangent line to a polar curve is given by r = sec(theta) * (d/dtheta)(r) at the point of tangent. This means that the slope of the tangent line is equal to the derivative of the polar curve at that particular point.

2. How do I find the point of tangency on a polar curve?

To find the point of tangency on a polar curve, you can equate the derivative of the polar curve to the slope of the tangent line and solve for theta. This will give you the value of theta at the point of tangency. Substituting this value into the original polar equation will give you the coordinates of the point of tangency.

3. Can the equation of a tangent line to a polar curve be negative?

Yes, the equation of a tangent line to a polar curve can be negative. This simply means that the tangent line is below the x-axis. However, the slope of the tangent line cannot be negative, as the derivative of a polar curve is always positive.

4. Is there a specific method for finding the equation of a tangent line to a polar curve?

Yes, there is a specific method for finding the equation of a tangent line to a polar curve. This involves taking the derivative of the polar curve, equating it to the slope of the tangent line, solving for theta, and then substituting this value into the original polar equation to find the coordinates of the point of tangency.

5. Can the equation of a tangent line to a polar curve be simplified?

Yes, the equation of a tangent line to a polar curve can be simplified by using trigonometric identities. For example, if the derivative of the polar curve contains a product of trigonometric functions, you can use the double angle or half angle identities to simplify the equation. Additionally, you can use the Pythagorean identity to eliminate any squares in the equation.

Similar threads

Quadratics Having a Common Tangent
    • Calculus and Beyond Homework Help
Replies
1
Views
328
Write the tangent lines to the curve
    • Calculus and Beyond Homework Help
Replies
1
Views
910
How to find the straight tangent line?
    • Calculus and Beyond Homework Help
Replies
6
Views
807
Find the equation of the tangent plane and normal to a surface
    • Calculus and Beyond Homework Help
Replies
1
Views
261
Find the two points on the curve that share a tangent line
    • Calculus and Beyond Homework Help
Replies
9
Views
1K
At what ##x## value is the tangent equally inclined to the given curve?
    • Calculus and Beyond Homework Help
Replies
5
Views
332
Finding the equation of a tangent line in polar coordinates?
    • Calculus and Beyond Homework Help
Replies
1
Views
4K
Find Values of Osculating Circle Tangent to a Parabola
    • Calculus and Beyond Homework Help
Replies
4
Views
320
Precise definition of tangent line to a curve
    • Precalculus Mathematics Homework Help
Replies
18
Views
1K
Finding the horizontal tan() lines of this equation
    • Calculus and Beyond Homework Help
Replies
3
Views
951

Hot Threads

Recent Insights

Back
Top