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Explain a situation where we would convert an equation from a product to a sum, and give an example.
For the following exercises, rewrite the product as a sum or difference.
For the following exercises, rewrite the sum or difference as a product.
For the following exercises, evaluate the product for the following using a sum or difference of two functions. Evaluate exactly.
For the following exercises, evaluate the product using a sum or difference of two functions. Leave in terms of sine and cosine.
For the following exercises, rewrite the sum as a product of two functions. Leave in terms of sine and cosine.
For the following exercises, prove the identity.
For the following exercises, rewrite the sum as a product of two functions or the product as a sum of two functions. Give your answer in terms of sines and cosines. Then evaluate the final answer numerically, rounded to four decimal places.
For the following exercises, algebraically determine whether each of the given expressions is a true identity. If it is not an identity, replace the right-hand side with an expression equivalent to the left side. Verify the results by graphing both expressions on a calculator.
For the following exercises, simplify the expression to one term, then graph the original function and your simplified version to verify they are identical.
For the following exercises, prove the following sum-to-product formulas.
Start with
Make a substitution and let
and let
so
becomes
Since and we can solve for and in terms of x and y and substitute in for and get
For the following exercises, prove the identity.
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