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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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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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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Q11:
Use DeMoivreβs 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 DeMoivreβs theorem, find the exact value of .
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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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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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