Feb 25­11:56 AM
6.4 Product-to-Sum and
Sum-to-Product Identities
Name: __________________
Objectives: Students will be able to verify trigonometric
identities involving multiple angles using the product-to-sum and
sum-to-product formulas.
Product-to-Sum Identities
cosxcosy = (1/2)[cos(x - y) + cos(x + y)]
sinxsiny = (1/2)[cos(x - y) - cos(x + y)]
sinxcosy = (1/2)[sin(x + y) + sin(x - y)]
cosxsiny = (1/2)[sin(x + y) - sin(x - y)]
Feb 18­11:43 AM
1
Examples Use the product-to-sum identities to rewrite each
expression as the sum or difference of two functions. Simplify
where possible.
1.) cosxsinx
2.) sin(3π/8)cos(π/8)
3.) Find the exact value of cos105osin75o.
Feb 18­11:59 AM
Sum-to-Product Identities
cosx + cosy = 2cos x + y cos x - y
2
2
cosx - cosy = -2sin x + y sin x - y
2
2
sinx + siny = 2sin x + y cos x - y
2
2
sinx - siny = 2sin x - y cos x + y
2
2
Feb 18­12:00 PM
2
Examples Use sum-to-product identities to rewrite each expression
as a product. Simplify where possible.
1.) sin22o + sin8o
2.) cos(π/12) + cos(π/3)
3.) sin5x - sin3x
Assignment: Page 602: 7 - 39 every other odd
Feb 18­12:07 PM
Feb 25­12:27 PM
3