Angle Between Polar Curves

Pre-requisites For Angle Between Polar Curves
Sign of Trigonometric Identities
8 Topics
Sign of Trigonometric Identities – Introduction
Sign of Trigonometric Identities – Quad I
Sign of Trigonometric Identities – Quad II
Sign of Trigonometric Identities – Quad III
Sign of Trigonometric Identities – Quad IV
Sign of Trigonometric Identities – Summary
Sign of Trigonometric Identities – 1
Sign of Trigonometric Identities – 2
General solution for Trigonometric ratios
4 Topics
General solution for Trigonometric ratios (Example 1)
General solution for Trigonometric ratios (Example 2)
General solution for Trigonometric ratios (Example 3)
General solution for Trigonometric ratios (Example 4)
Concept of Derivative – Slope
2 Topics
Concept of Derivative – Slope – St line
Concept of derivative – slope – curve
Differentiation of Basis functions
14 Topics
Introduction – Chain and Quotient Rules
Derivative of tan x
Derivative of sec x
Derivative of cosec x
Derivative of cot x
Derivative of [y = e^x * x^n]
Derivative of [y = tan^(-1) x
Derivative of [y = x/(ax+b)] – Quotient rule
Derivative of [y = x/(ax+b)] – Chain rule
Derivative of [x^2 + y^2 = k]
Derivative of [y = 1/sqrt(ax^2 +b)]
Derivative of [y = a^x (log (1+x^2))]
Derivative of [y = a^sinx (1+sin^2 (x)) sec x]
Graphical understanding of trigonometric derivatives
Applications of Derivatives
7 Topics
Finding nature of the curve
Interpreting curvature of a curve
Linearization of a curve
L-Hospital Rule
Use of second derivative (curvature)
Maxima & Minima – 1
Maxima & Minima – 2
Angle between Curves & Radius of curvature
5 Topics
Essential trigonometric identities 1
Essential trigonometric identities 2
Essential trigonometric identities 3
Essential trigonometric identities 4
Essential trigonometric identities 5
Angle Between Polar Curves
Introduction to Polar Curves
1 Topic
Introduction
Polar and Cartesian Equivalence
1 Topic
Polar and Cartesian Equivalence
Converting Cartesian and Polar Curves
5 Topics
Parabola – Cartesian to Polar
Circle – Polar to Cartesian
Offset Circle – Cartesian to Polar
Cardioid – Polar and Cartesian Equivalence
Rose Curve – Polar and Cartesian Equivalence
Parametric Equation for Cycloid
1 Topic
Visualizing the Cycloid formation
Parametric Equation for Ellipse
1 Topic
Parametric Equation for Ellipse
Polar curves
10 Topics
Introduction to angle between curves
Evolution of angle between geometric entities
Angle between radius and tangent vector – Purpose Definition
Angle between radius and tangent vector – Understanding the Figure
Angle between radius and tangent vector – Strategy
Angle between radius and tangent vector – Derivation
Angle between radius and tangent vector – Derivation 1 and Common Mistakes
Angle between radius and tangent vector – Incidental Facts
Angle between radius and tangent vector – Memory Structure
Procedure for angle between two curves
Solving angle between Curves
12 Topics
Problem 1 (Circle)
Problem 1 – Method 2 (Circle)
Problem 2 (Cardioid)
Problem 2 – Critical Observations
Problem 3
Problem 4
Problem 4 (Method 2)
Problem 5 (Parabola)
Problem 6 (Cardioid Slope)
Problem 7
Problem 8
Unravelling the Examiner’s Mind
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General solution for Trigonometric ratios (Example 1)

Angle Between Polar Curves General solution for Trigonometric ratios General solution for Trigonometric ratios (Example 1)

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