Using Demoivre to Prove Trigonometric Identities Simplified Revision Notes for Leaving Cert Mathematics

Revision notes with simplified explanations to understand Using Demoivre to Prove Trigonometric Identities quickly and effectively.

Learn about DeMoivre's Theorem for your Leaving Cert Mathematics Exam. This Revision Note includes a summary of DeMoivre's Theorem for easy recall in your Mathematics exam

460+ students studying

Using Demoivre to Prove Trigonometric Identities

De Moivre's can be used to prove trigonometric identities.

Example

infoNote

Use de Moivre's theorem to prove the identity $(\cos \theta + i \sin \theta)^3 = \cos(3\theta) + i \sin(3\theta)$ .

Expand the left hand side :

(\cos \theta + i \sin \theta)^3 = \cos^3 \theta - 3 \cos \theta \sin^2 \theta + i (3 \cos^2 \theta \sin \theta - \sin^3 \theta)

Compare real with real, imaginary with imaginary :

\cos(3 \theta) = \cos^3 \theta - 3 \cos \theta \sin^2 \theta

\sin(3 \theta) = 3 \cos^2 \theta \sin \theta - \sin^3 \theta

500K+ Students Use These Powerful Tools to Master Using Demoivre to Prove Trigonometric Identities For their Leaving Cert Exams.

Enhance your understanding with flashcards, quizzes, and exams—designed to help you grasp key concepts, reinforce learning, and master any topic with confidence!

150 flashcards

Flashcards on Using Demoivre to Prove Trigonometric Identities

Revise key concepts with interactive flashcards.

Try Mathematics Flashcards

10 quizzes

Quizzes on Using Demoivre to Prove Trigonometric Identities

Test your knowledge with fun and engaging quizzes.

Try Mathematics Quizzes

29 questions

Exam questions on Using Demoivre to Prove Trigonometric Identities

Boost your confidence with real exam questions.

Try Mathematics Questions