# 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 Euler’s formula to express in terms of .

Hint: First write and in terms of and .

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Q2:

Using Euler’s formula, express in terms of .

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Q3:

Using Euler’s formula, derive a formula for and in terms of and .

• A,
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Q4:

Using Euler’s 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 Euler’s formula, express in the form , where , , and are constants to be found.

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Q7:

Using Euler’s formula, express in terms of sine and cosine.

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Q8:

What trigonometric identities can be derived by applying Euler’s identity to ?

• A,
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Q9:

Use Euler’s 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 Euler’s formula to derive a formula for and in terms of and .

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Hence, express in terms of .

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This lesson includes 9 additional questions and 18 additional question variations for subscribers.