Some problems require the reverse of the process we just used. The
sum-to-product formulas allow us to express sums of sine or cosine as products. These formulas can be derived from the product-to-sum identities. For example, with a few substitutions, we can derive the sum-to-product identity for
sine . Let
and
Then,
Thus, replacing
and
in the product-to-sum formula with the substitute expressions, we have
The other sum-to-product identities are derived similarly.
Sum-to-product formulas
The
sum-to-product formulas are as follows:
Writing the difference of sines as a product
Write the following difference of sines expression as a product:
We begin by writing the formula for the difference of sines.
Substitute the values into the formula, and simplify.
t he silly nut company makes two mixtures of nuts: mixture a and mixture b. a pound of mixture a contains 12 oz of peanuts, 3 oz of almonds and 1 oz of cashews and sells for $4. a pound of mixture b contains 12 oz of peanuts, 2 oz of almonds and 2 oz of cashews and sells for $5. the company has 1080
Lairene and Mae are joking that their combined ages equal Sam’s age. If Lairene is twice Mae’s age and Sam is 69 yrs old, what are Lairene’s and Mae’s ages?