Transcript Verifying Trigonometric Identities

Verifying Trigonometric
Identities
Section 5.2
Math 1113
Created & Presented by Laura Ralston
Verifying Trigonometric Identities

In this section, we will study techniques
for verifying trigonometric identities.

The key to verifying identities is the ability
to use the fundamental identities and
rules of algebra to rewrite trigonometric
expressions
Review
Algebraic Expression:  Equation: a
a collection of
statement that two
numbers, variables,
mathematical
symbols for
expressions are equal.
operations, and
grouping symbols;
x+2=5
contains no equal sign
2(4x -3) – 6
sin x = 0
2sin(4x – p) + 3

Three Categories of Equations

Contradiction: no
values of the variable
make the equation
true

Conditional: only 1 or
several values of the
variable make the
equation true
x+2=x
x + 2 = 5 ---- x = 3
sin x = 5
sin x = 0 ----- x = 0

Identity: equation is true for EVERY value
of the variable
x + x = 2x
2x = 2x
cos2x + sin2x = 1

Verifying an Identity is quite different from
solving an equation.

There is no well-defined set of rules to
follow in verifying trigonometric identities
and the process is best learned by
practice!!!
Guidelines for Verifying Trig
Identities

Work with one side of the identity at a
time. It is often better to work with the
more complicated side first.

Look for opportunities to factor an
expression, add fractions, square a
binomial, or create a monomial
denominator.
Look for opportunities to use the
fundamental identities. Note which
functions are in the final expression you
want.
 Sines and cosines pair up well, as do
secants and tangents, and cosecants and
cotangents.


If all else fails, try converting all terms to
sines and cosines.

Always try something!! Even paths that
lead to dead ends give you insights.

There can be more than one way to verify
an identity. Your method may differ from
that used by your instructor or classmates.

This is a good chance to be creative and
establish your own style, but try to be as
efficient as possible.