# 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 Moivreβs theorem, find the exact value of

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**Q2: **

Which of the following is equivalent to ?

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**Q3: **

Use de Moivreβs theorem to find the exact value of .

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**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 Moivreβs theorem to express in terms of power of and .

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**Q6: **

Use de Moivreβs 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 Moivreβs 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 Moivreβs theorem to express in terms of power of .

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