A bicycle wheel has 24 evenly spaced spokes. Use two methods to find the exact value of , where is the angle between consecutive spokes. For the first method, use the half-angle identity for cosine. For the second, use the angle difference formula for cosine. What do you notice about the two resulting numerical expressions for ?

Find , the angle between consecutive spokes.

Find the exact value of by using the half-angle identity for cosine.

Find the exact value of by using the angle difference formula for cosine.

Compare the two expressions for . Use a calculator to verify that the results of the two expressions are equivalent.

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