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:
1- sec q
2
Trigonometric Identities
Mr. Lopez
April 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
1
sin q
cscq =
tanq =
sinq
cosq
1
secq =
cosq
cosq cot q =
sinq
1
cot q =
tan q
Pythagorean
Identities
NegativeAngle
Identities
sin 2 q + cos2 q =1
1) (Sin x)^2 = 1-(cos x)^2
1)
sin (-x) = - sin x
* csc (-x) = - csc x
2) (cos x)^2 = 1-(sin x)^2
1+ tan2 q = sec2 q
1) (tan x)^2 = (sec x)^2 - 1
2) cos (-x) = cos x
*sec (-x) = sec x
2) 1 = (sec x)^2 – (tan x)^2
cot q +1= csc q
3) tan (-x) = - tan x
1) (cot x)^2 = (csc x)^2 - 1
*cot (-x) = - cot (x)
2
2
2) 1= (csc x)^2 –(cot x)^2
Guided Practice
 1) Prove the identity: (sec x)*(sin x) = tan x
 2) Prove the identity:
 3) Prove the identity:
sin x(cot x + tan x) = sec x
(sec x -1)(sec x +1) = tan2 x
Your Turn!!
 1) Prove the second Pythagorean Theorem.
 2) Prove the third Pythagorean Theorem.
sin x
1= cos x
1+ cos x
2
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.
*