Rewriting a trigonometric expression using the difference of squares
Rewrite the trigonometric expression:
Notice that both the coefficient and the trigonometric expression in the first term are squared, and the square of the number 1 is 1. This is the difference of squares. Thus,
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 by simplifying an expression and then verifying 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?
if three forces F1.f2 .f3 act at a point on a Cartesian plane in the daigram .....so if the question says write down the x and y components ..... I really don't understand
a fixed gas of a mass is held at standard pressure temperature of 15 degrees Celsius .Calculate the temperature of the gas in Celsius if the pressure is changed to 2×10 to the power 4