Double Angle Identity Activity

Investigate the following things

1. Relationship between Angle [math]\beta[/math] and angle [math]\alpha[/math][br][br]2. Determine the lengths of EF and DF using triangle DEF in terms of angle [math]\alpha[/math][br][br]3. Determine the lengths of GC, GD and GE in terms of angle [math]\beta[/math]

1.

Choose the correct option

[math]\alpha[/math]= 2[math]\beta[/math] [math]\beta[/math]= 2[math]\alpha[/math] [math]\alpha[/math]=[math]\beta[/math]

2. From Triangle DEF

What is EF and DF

DF= cos( [math]\alpha[/math] ) EF= sin( [math]\alpha[/math] ) DF= sin( [math]\alpha[/math] ) and EF = cos ( [math]\alpha[/math] ) DF= cos( [math]\beta[/math] ) and EF= sin( [math]\beta[/math])

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

GC = cos( [math]\beta[/math] ) and GE = sin( [math]\beta[/math] ) GC= cos( [math]\alpha[/math] ) and GE = sin( [math]\alpha[/math] )

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([math]\alpha[/math]) and cos([math]\beta[/math])

cos([math]\alpha[/math]) = 2cos[sup]2[/sup] ( [math]\beta[/math]) +1 cos(2[math]\beta[/math]) = 2 cos[sup]2[/sup] ([math]\beta[/math]) -1 1+cos([math]\alpha[/math]) = 2 cos[sup]2 [/sup] ([math]\beta[/math])

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.[br]( Try to rewrite them in terms of angles)

Double Angle Identity Activity

Investigate the following things

1.

2. From Triangle DEF

3. What are the lengths of GC and GE

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

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

Discussion

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An Investigaton_ Double Angle Identity

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