1. Ch 7 – Trigonometric Identities and Equations
7.1 – Basic Trig Identities

2. Some Vocab
Identity: a statement of equality between two expressions that is true for all values of the variable(s)
Trigonometric Identity: an identity involving trig expressions
Counterexample: an example that shows an equation is false.

3. Prove that sin(x)tan(x) = cos(x) is not a trig identity by producing a counterexample.
You can do this by picking almost any angle measure.
Use ones that you know exact values for:
 0, π/6, π/4, π/3, π/2, and π

4. Reciprocal Identities

5. Quotient Identities

6. Do you remember the Unit Circle?
What is the equation for the unit circle?
x2 + y2 = 1
What does x = ? What does y = ?
(in terms of trig functions)
sin2θ + cos2θ = 1
Pythagorean Identity!

7. Take the Pythagorean Identity and discover a new one!
Hint: Try dividing everything by cos2θ
sin2θ + cos2θ =
cos2θ cos2θ cos2θ
tan2θ = sec2θ
Quotient
Identity
Reciprocal
Identity
another Pythagorean Identity

8. Take the Pythagorean Identity and discover a new one!
Hint: Try dividing everything by sin2θ
sin2θ + cos2θ =
sin2θ sin2θ sin2θ
cot2θ = csc2θ
Quotient
Identity
Reciprocal
Identity
a third Pythagorean Identity

9. Opposite Angle Identities
sometimes these are called even/odd identities

10. Simplify each expression.

11. Using the identities you now know, find the trig value.
If cosθ = 3/4, If cosθ = 3/5, find secθ. find cscθ.

12. sinθ = -1/3, 180o < θ < 270o; find tanθ secθ = -7/5, π < θ < 3π/2; find sinθ

13. Homework
To no surprise, there is a change: 7.1 – Basic Trig Identities Please do pages : #19-37 odds #44, 45, 48, 49, 50, 51