After working hard to solve an
algebra
problem you check the answer and it looks different from yours. But
after a
moment of panic, you realize that it’s really just saying the same
thing in a
different way. This can often be seen by means of an algebraic identity
(i.e.
an equation, like x^2+2x+1=(x+1)^2,
which is true for all values of the variable). You also
frequently use identities to simplify expressions and to rearrange the
terms in
an equation to make it easier to find a solution.
Identities involving
trigonometric
functions are important for similar reasons. You have already seen some
examples, and in this section you will find more, and will also learn
how to
work with identities you know in order to get new ones.
1. Read section 6.1 of the text.
2. Read the following Study Notes and Discussion (and whatever text sections they refer you to), and make sure that you have absorbed the main points by answering the questions.
3.
Read
sections 6.3, and 6.4 of the text.
4.
Follow
the instructions regarding Practice.
When you
have met the Learning
Objectives for this
Section, go on
to the next.