Lesson Worksheet: Euler’s Formula for Trigonometric Identities Mathematics
In this worksheet, we will practice using Euler’s formula to prove trigonometric identities like double angle and half angle.
Q1:
Use Eulerโs formula to express in terms of .
Hint: First write and in terms of and .
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Q2:
Using Eulerโs formula, express in terms of .
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Q3:
Using Eulerโs formula, derive a formula for and in terms of and .
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Q4:
Using Eulerโs formula, express in the form , where , , and are constants to be found.
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Q5:
Express and in terms of and .
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Q6:
Using Eulerโs formula, express in the form , where , , and are constants to be found.
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Q7:
Using Eulerโs formula, express in terms of sine and cosine.
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Q8:
What trigonometric identities can be derived by applying Eulerโs identity to ?
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Q9:
Use Eulerโs formula to express in terms of sine and cosine.
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Given that , what trigonometric identity can be derived by expanding the exponentials in terms of trigonometric functions?
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Q10:
Use Eulerโs formula to derive a formula for and in terms of and .
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Hence, express in terms of .
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