Angle between Two Polar Curves - Polar Curves - Engineering Mathematics - 2 | Summary and Q&A

TL;DR

Learn how to find the angle between two curves in a polar coordinate system using the tangent of the curves at their point of intersection.

Key Insights

• 🔺 The angle of intersection between two curves in a polar coordinate system is calculated by finding the difference between the angles of the tangents at their point of intersection.
• 🔺 If the tangents of the curves are perpendicular, the angle of intersection is 90 degrees.
• 🔺 If the equations of the curves can be explicitly solved for the angles, the angle of intersection can be calculated using trigonometric identities.

Transcript

hello in this session we'll talk about angle between two curves so let us say that in our polar coordinate system we have two curves here which will intersect at some point and let's say that point is p so let's say the first polar curve is r equal to f1 theta the second one is r2 equal to f2 theta p point of intersection for the polar curve let th... Read More

Questions & Answers

Q: How is the angle of intersection between two curves in a polar coordinate system calculated?

The angle of intersection can be found by subtracting the angles of the tangents of the curves at their point of intersection.

Q: What if the tangents of the curves are perpendicular?

If the tangents are perpendicular, the angle of intersection is 90 degrees.

Q: How can the angle of intersection be calculated if the equations of the curves are given?

By taking the logarithm of the equations, differentiating with respect to theta, and using trigonometric identities, the angles of the tangents can be found and then subtracted to calculate the angle of intersection.

Q: What if the equations of the curves cannot be explicitly solved for the angles?

In such cases, the point of intersection of the curves can be found, and the tangents at that point can be used to calculate the angle of intersection.

Summary & Key Takeaways

• Two polar curves intersect at a common point P in a polar coordinate system.

• The angle of intersection between the curves can be found by subtracting the angles of the tangents of the curves at point P.

• If the tangents of the curves are perpendicular, the angle of intersection is 90 degrees.