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

TL;DR

The video explains how to find the angle of intersection between two polar curves using logarithmic differentiation and equation solving.

Key Insights

• 🐻‍❄️ Logarithmic differentiation is a useful technique for differentiating polar equations.
• 😥 Equating two equations and solving for theta can help determine the point of intersection between polar curves.
• 😑 The expressions cot(phi) = -cot(2theta) and cot(phi) = cot(2theta) can be used to find the angle of intersection.

Transcript

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Questions & Answers

Q: What is the purpose of taking logarithms of the equations in this problem?

Taking logarithms of the equations allows us to simplify the differentiation process and make it easier to solve for theta.

Q: How is the angle of intersection related to the expressions cot(phi) = -cot(2theta) and cot(phi) = cot(2theta)?

The expressions cot(phi) = -cot(2theta) and cot(phi) = cot(2theta) relate the angle phi to the angle of intersection. By solving for theta using these expressions, we can find the angle of intersection.

Q: How are the two polar curves, r^2 sin(2theta) = 4 and r^2 = 16 sin(2theta), represented mathematically?

The first polar curve is represented by r^2 sin(2theta) = 4, and the second polar curve is represented by r^2 = 16 sin(2theta).

Q: How is the point of intersection of the two curves found?

To find the point of intersection, the equations representing the two curves (r^2 sin(2theta) = 4 and r^2 = 16 sin(2theta)) are equated to each other, and then the equation is solved for theta.

Summary & Key Takeaways

• The video discusses the process of finding the angle of intersection between two polar curves using logarithmic differentiation and equation solving.

• Logarithmic differentiation is used to differentiate the equations with respect to theta.

• Then, the equations are equated to find the point of intersection, from which the angle of intersection can be determined.