Do Now
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.