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# Angle between Polar curves

149.00

Validity: 45 days

This topic includes the important derivation of angle between radius vector and tangent, converting Cartesian and parametric curves to polar form, problems on angle between curves with graphical visualization.

Salient features of this module are:

• Pre-requisites to polar curves
• Graphical visualization
• Concept testing
• Unravelling examiners mind
• Memory structure (for derivations)
• Model question paper

### Course Contents:

Pre-requisites to Elements of Differential Calculus

• Sign of Trigonometric Identities
• 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
• 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 derivate – Slope
• Concept of Derivative – Slope – Straight line
• Concept of Derivative – Slope – Curve
• Differentiation of Basic functions
• 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
• Application of Derivative
• 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
• 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
• Introduction
• Polar and Cartesian Equivalence
• Polar and Cartesian Equivalence
• Converting Cartesian and Polar curves
• 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
• Visualizing the Cycloid formation
• Parametric Equation for Ellipse
• Parametric Equation for Ellipse
• Polar Curves
• 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
• 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 Examiners Mind

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