How Can the Unit Circle Prove the Cosine Half-Angle Formula?

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The discussion focuses on proving the cosine half-angle formula, cos(θ/2) = ±√((1 + cos(θ))/2), using the unit circle. Participants suggest analyzing points A, B, C, and D on the unit circle, where A represents (cos(t), sin(t)) and B represents (cos(t/2), sin(t/2)). The key approach involves demonstrating that the midpoint of segment AC lies on segment BD. Visual aids, such as graphs, are requested to enhance understanding of the proof. The conversation emphasizes the geometric interpretation of the formula through the properties of the unit circle.
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Homework Statement



Prove that cos(\frac{\theta}{2}) = \pm\sqrt{\frac{1+cos\theta}{2}} using the unit circle.


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The Attempt at a Solution



I'm not sure if it's possible for you to provide a clear graph on here for the solution but a link would also be nice :)

View attachment half angle.bmp
 
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consider the points A=(cos(t),sin(t)) B=(cos(t/2),sin(t/2)) C=(1,0) D=(0,0)
To find B show that the midpoint of the segment AC is on the segment BD
 

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