1. Simple Trig Identities
Lesson 2.4b

2. Definition of An Identity
Any equation that is true for every number in the domain of the equation.
Example
2x + 12 = 2(x + 6)
Trig identities
Ratio Identities
Reciprocal identities
Pythagorean identities

3. Ratio Identities
Since we know that x = cos t and y = sin t …

4. Reciprocal Identities
Identities given by definition

5. Pythagorean Identities
Consider that x2 + y2 = 1
Thus
Similarly

6. Working with Identities
Simplifying expressions using identities
Given
Simplify
Give a justification for each step

7. Working with Identities
Tips
In an expression, look for a part of the expression that looks like part of one of the identities
Substitute that in
Look for factors to cancel
Look for terms of an expression that can be combined to form one of the identities
Also possible to look at identities in different forms

8. Experiment with what your calculator does with these expressions
Practice
Try these
Experiment with what your calculator does with these expressions

9. Assignment
Lesson 2.4b
Page 167
Exercises 55 – 97 odd