There are multiple ways to represent a trigonometric expression. Verifying the identities illustrates how expressions can be rewritten to simplify a problem.
Graphing both sides of an identity will verify it. See
[link] .
Simplifying one side of the equation to equal the other side is another method for verifying an identity. See
[link] and
[link] .
The approach to verifying an identity depends on the nature of the identity. It is often useful to begin on the more complex side of the equation. See
[link] .
We can create an identity and then verify it. See
[link] .
Verifying an identity may involve algebra with the fundamental identities. See
[link] and
[link] .
Algebraic techniques can be used to simplify trigonometric expressions. We use algebraic techniques throughout this text, as they consist of the fundamental rules of mathematics. See
[link] ,
[link] , and
[link] .
Section exercises
Verbal
We know
is an even function, and
and
are odd functions. What about
and
Are they even, odd, or neither? Why?
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?