# Worksheet: De Moivre’s Theorem for Trigonometric Identities

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

Q1:

Using de Moivreβs theorem, find the exact value of

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• E

Q2:

Which of the following is equivalent to ?

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Q3:

Use de Moivreβs theorem to find the exact value of .

• A0
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• C5
• D
• E1

Q4:

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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Q5:

Use de Moivreβs theorem to express in terms of power of and .

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Q6:

Use de Moivreβ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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Q7:

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

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Q8:

Use de Moivreβs theorem to express in terms of power 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:

Use de Moivreβs theorem to express in terms of power of .

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Q11:

Use DeMoivreβs theorem to express in terms of powers of .

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Q12:

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

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Q13:

Using DeMoivreβs theorem, find the exact value of .

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• D

Q14:

Express in terms of powers of and .

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Q15:

Express in terms of powers of and .

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Q16:

Express in terms of the sines of multiples of .

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• D

Q17:

Express in terms of the cosines of multiples of .

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Q18:

Express in terms of the sines of multiples of .

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