# Double Angle Identity Activity

- Author:
- Satvinder Singh

- Topic:
- Trigonometry

## Investigate the following things

1. Relationship between Angle and angle
2. Determine the lengths of EF and DF using triangle DEF in terms of angle
3. Determine the lengths of GC, GD and GE in terms of angle

## 1.

Choose the correct option

## 2. From Triangle DEF

What is EF and DF

## 3. What are the lengths of GC and GE

Choose the correct option, Hint: Radius of a semicircle is unity and the CE = 1 unit

## 4 Use Triangle CDF,Use pen and paper (Remember CE= 1 unit and CD = 2 GC)

Apply Pythagoras theorem to work out the relationship between cos() and cos()

## 5. if Triangle ECG and Triangle DCF are similar ( think why)

then using the ratio of sides establish a relationship between DF, GE and DC. ( Try to rewrite them in terms of angles)

## Discussion

For every result discuss your findings with your classmates and teacher.