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Radians & Degrees

Trig. Definitions using {x, y, r}

Trig. Definitions using Unit Circle

Trig. Functions & Graphs

Transformations

Trig. Identities

Trig. Equations

Summary&Test

 

jdsmathnotes

 


 UNIT 7 : TRIGONOMETRIC FUNCTIONS

 LESSON 6 : TRIGONOMETRIC IDENTITIES

 

 

Definition: An Identity is a mathematical statement that is true for all values of the variable in the given domain.

 

Example 1: x2 + x = x(x + 1)

This statement is an identity as it is true for all x in the real number system

 

Proof: We prove this by showing that the Left side of the equation equals the Right side.

 

L.S. = x2 + x R.S. = x(x + 1)

= x2 + x

Therefore L.S. = R.S. and the identity is proven.

 

Basic Trigonometric Identities :

 

 

 

 

 

 

 

Example 2:

 

Proof:

Text Box: Strategies for Proving Trig. Identities
1.	Start with the most complex side.  You may, however work on either side.
2.	Change any tan x or cot x expression to sin x and cos x using the quotient identities.
3.	Change any sec x or csc x expression to sin x and cos x using the reciprocal identities.
4.	Simplify algebraically using expanding or factoring where appropriate
5.	Use rules of fractions where needed  common denominators, multiplication and division rules for fractions.
6.	If sin2x or cos2x etc.  occurs, use the Pythagorean identities if they simplify the expression.
This should be done if the number 1 occurs with the squared expression.
 

 

 

 

 

 

 

 

 

 

 

 

 


Example 3:

 

Proof:

 

 

 

 

 

 

 

 

 

 

 

 

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