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Take out Extra Credit Assignment from Mrs. Cheung

Reminder: Office Hours from 3:30 to 4:30pm

Warm Up

1) Write down 3 Reciprocal Identities

2) Write down 2 Tangent and Cotangent Identities

3) Write down 1 Pythagorean Identity

4) Using known identities to simplify the following:

Trigonometric IdentitiesMr. LopezApril 24, 2014

Students will be able to…

Use algebra to simplify trigonometric expressions and to establish identities by applying the Reciprocal Identities, Pythagorean Identities, and Negative-Angle Identities.

Essential Questions

What is an identity?

How do we prove trigonometric identities?

How do we simply trigonometric expressions?

Reciprocal Identities

Tangent and Cotangent Ratio Identities

Pythagorean Identities

Negative-Angle Identities

1) (Sin x)^2 = 1-(cos x)^2

2) (cos x)^2 = 1-(sin x)^2

1) sin (-x) = - sin x

* csc (-x) = - csc x

1) (tan x)^2 = (sec x)^2 - 1

2) 1 = (sec x)^2 – (tan x)^2

2) cos (-x) = cos x

*sec (-x) = sec x

1) (cot x)^2 = (csc x)^2 - 1

2) 1= (csc x)^2 –(cot x)^2

3) tan (-x) = - tan x

*cot (-x) = - cot (x)

Guided Practice

1) Prove the identity: (sec x)*(sin x) = tan x

2) Prove the identity:

3) Prove the identity:

Your Turn!!

1) Prove the second Pythagorean Theorem.

2) Prove the third Pythagorean Theorem.

Hint: Use the first Pythagorean Theorem.

Challenge:

3) Prove the following identity:

Math Fair!! ---30 min

Get your handout from Wednesday

Select your partners

Division of Labor

Research Ideas related to Trig

Possible Topics: See Chapters 6, 7 and especially 8

Select a topic….Be Specific and Creative!!!!

Independent Practice

Review pg. 459, specifically the table of identities.

Read pg. 463, Guidelines for Establishing Identities.

Do brain exercises: 9, 11, 13, 19, 23, 27, 49, 53 and 69 on page 464-465

Note: For these 10 exercises, show all steps and justify each step.

*If you finish early, work on math fair project.