# UCSS Math II 5.9.5 Example 4

- Author:
- Walch Education

- Topic:
- Cosine

The potential energy in joules of an oscillating spring can be represented by the expression , where is a constant and is the time in seconds since the spring began oscillating. Create a two-column proof to show that the potential energy of the spring can also be written as .

- Create the outline for the two-column proof.
- Rewrite the fraction on the left side of the equation as the difference of two fractions.
- Simplify
. - Use the reciprocal identity
to rewrite the expression from step 3. - Use the Pythagorean identity
to rewrite the expression . - Fill in the columns of the two-column proof.

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