# Worksheet: Euler's Formula for Trigonometric Identities

In this worksheet, we will practice using Euler's formula to prove trigonometric identities like double angle and half angle.

**Q1: **

Using Eulerโs formula, express in terms of .

- A
- B
- C
- D
- E

**Q2: **

Using Eulerโs formula, express in the form , where , , and are constants to be found.

- A
- B
- C
- D
- E

**Q3: **

Using Eulerโs formula, derive a formula for and in terms of and .

- A ,
- B ,
- C ,
- D ,
- E ,

**Q4: **

Using Eulerโs formula, express in the form , where , , and are constants to be found.

- A
- B
- C
- D
- E

**Q5: **

Express and in terms of and .

- A ,
- B ,
- C ,
- D ,
- E ,

**Q6: **

Use Eulerโs formula to express in terms of .

*Hint*: First write and in terms of and .

- A
- B
- C
- D
- E

**Q7: **

Using Eulerโs formula, express in terms of sine and cosine.

- A
- B
- C
- D
- E

**Q8: **

What trigonometric identities can be derived by applying Eulerโs identity to ?

- A ,
- B ,
- C ,
- D ,
- E ,