# Lesson Worksheet: De Moivre’s Theorem for Trigonometric Identities Mathematics

In this worksheet, we will practice using de Moivre’s theorem to obtain trigonometric identities.

Q1:

Express in terms of the sines of multiples of .

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Q2:

Which of the following is equivalent to ?

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Q3:

Using de Moivre’s theorem, find the exact value of .

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Q4:

Use de Moivre’s theorem to express in terms of power of and .

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Q5:

Express in terms of powers of and .

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Q6:

Express in terms of , , , , , , and any constant terms.

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Q7:

Use de Moivre’s theorem to express in terms of powers of .

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By considering the solutions of , find an exact representation for .

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Q8:

Using de Moivre’s theorem, find the exact value of

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Q9:

Express in terms of powers of and .

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Express in terms of powers of and .

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Hence, express in terms of powers of .

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Q10:

Express in the form , where ,, and are constants to be found.

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Hence, find all the solutions of in the interval . Give your answers in exact form.

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This lesson includes 18 additional questions and 23 additional question variations for subscribers.