DeMoivre's Theorem (Leaving Cert Mathematics): Flashcards

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Using Demoivre to Prove Trigonometric Identities
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Use of De Moivre's theorem

Prove trigonometric identities

De Moivre: (cosheta+isinheta)3(cos heta + i sin heta)^3

cos(3heta)+isin(3heta)cos(3 heta) + i sin(3 heta)

First step in De Moivre proof method

Expand the left-hand side

What to compare in De Moivre method

Real with real, imaginary with imaginary

cos(3heta)cos(3 heta) in terms of coshetacos heta, sinhetasin heta

cos3heta−3coshetasin2hetacos^3 heta - 3 cos heta sin^2 heta

sin(3heta)sin(3 heta) in terms of coshetacos heta, sinhetasin heta

3cos2hetasinheta−sin3heta3 cos^2 heta sin heta - sin^3 heta

Real part of expanded (cosheta+isinheta)3(cos heta + isin heta)^3

cos3heta−3coshetasin2hetacos^3 heta - 3cos hetasin^2 heta

Imag. part of expanded (cosheta+isinheta)3(cos heta + isin heta)^3

3cos2hetasinheta−sin3heta3cos^2 hetasin heta - sin^3 heta

Explore Leaving Cert Mathematics Revision Notes by Topics

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Explore Leaving Cert Mathematics Model Answers by Topics

Fundamentals of Complex Numbers

The Basics

Argand Diagrams & Modulus

Solving Equations

DeMoivre's Theorem

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Explore Leaving Cert Mathematics Quizzes by Topics

Fundamentals of Complex Numbers

The Basics

Argand Diagrams & Modulus

Solving Equations

DeMoivre's Theorem

Transformations

Explore Leaving Cert Mathematics Exam Questions by Topics

Fundamentals of Complex Numbers

The Basics

Argand Diagrams & Modulus

Solving Equations

DeMoivre's Theorem

Transformations

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