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Level 1 Simplifying Identities Day 1.notebook 1 January 08, 2014 polar plane and graphing points Ch.8 Lesson 1

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Page 1: polar plane and - Miss Sahady PSHS Class Websitemisssahadypshsclasswebsite.weebly.com/uploads/5/1/... · 1 January 08, 2014 polar plane and graphing points Ch.8 Lesson 1 Level 1 Simplifying

Level 1 Simplifying Identities Day 1.notebook

1

January 08, 2014

polar plane and graphing points

Ch.8      Lesson 1 

Page 2: polar plane and - Miss Sahady PSHS Class Websitemisssahadypshsclasswebsite.weebly.com/uploads/5/1/... · 1 January 08, 2014 polar plane and graphing points Ch.8 Lesson 1 Level 1 Simplifying

Level 1 Simplifying Identities Day 1.notebook

2

January 08, 2014

Target

Agenda

Purpose

Evaluation

Agenda

Purpose

Evaluation

TSWBAT: Use the radius and angle to create the coordinate for a point on a polar plane and graph it

New Years Reflection and goal

Expectations (morning routine, bathroom, new passes,Self tracker, class environment, corrections, outline for semester

Lesson

BAT: look at information in a different way, graph really cool trig functions that are seen in the real world, better understanding of vectors

3-2-1

Page 3: polar plane and - Miss Sahady PSHS Class Websitemisssahadypshsclasswebsite.weebly.com/uploads/5/1/... · 1 January 08, 2014 polar plane and graphing points Ch.8 Lesson 1 Level 1 Simplifying

Level 1 Simplifying Identities Day 1.notebook

3

January 08, 2014

Warm-Up:1.

2.

On your Daily Sheet paper, tell me about the best thing that happened to you over break

On a separate sheet of paper, look through your quizzes, tests and corrections and write the 2nd letter to yourself about how you are doing in this class, what you have learned about studying and your abilities, and the goals you have for yourself until the end of the semester

Page 4: polar plane and - Miss Sahady PSHS Class Websitemisssahadypshsclasswebsite.weebly.com/uploads/5/1/... · 1 January 08, 2014 polar plane and graphing points Ch.8 Lesson 1 Level 1 Simplifying

Level 1 Simplifying Identities Day 1.notebook

4

January 08, 2014

 trıg expressıonsDef: ‐trig funcons, variables and constants 

 put together without an equal sign

Ex.   cosx – x

sin2 a + cos2a

1‐sec B  tanB

Page 5: polar plane and - Miss Sahady PSHS Class Websitemisssahadypshsclasswebsite.weebly.com/uploads/5/1/... · 1 January 08, 2014 polar plane and graphing points Ch.8 Lesson 1 Level 1 Simplifying

Level 1 Simplifying Identities Day 1.notebook

5

January 08, 2014

 sımplıfyıng trıg expressıonsDef: ‐Substung trig idenes in, to get down to 

one or two trig expressions

How it should look:Work Vercally down

orUse'implies' arrow ==> 

to work across

Page 6: polar plane and - Miss Sahady PSHS Class Websitemisssahadypshsclasswebsite.weebly.com/uploads/5/1/... · 1 January 08, 2014 polar plane and graphing points Ch.8 Lesson 1 Level 1 Simplifying

Level 1 Simplifying Identities Day 1.notebook

6

January 08, 2014

Wha

t are

we

goin

g

to u

se to

do

this

?

Page 7: polar plane and - Miss Sahady PSHS Class Websitemisssahadypshsclasswebsite.weebly.com/uploads/5/1/... · 1 January 08, 2014 polar plane and graphing points Ch.8 Lesson 1 Level 1 Simplifying

Level 1 Simplifying Identities Day 1.notebook

7

January 08, 2014

recıprocal ıdentıtıesDefinion ‐  idenes from trig funcon definions

Idendies:

sinA =    1           cosA=    1         tanA =    1                 cscA          secA      cotA

cscA =    1           secA =     1        cotA =    1                sinA            cosA       tanA

Page 8: polar plane and - Miss Sahady PSHS Class Websitemisssahadypshsclasswebsite.weebly.com/uploads/5/1/... · 1 January 08, 2014 polar plane and graphing points Ch.8 Lesson 1 Level 1 Simplifying

Level 1 Simplifying Identities Day 1.notebook

8

January 08, 2014

Simplify the expression‐Swap trig idenes, so that we have the least amount of trig funcons

ex. cos A secA 

ex. csc A             sin A 

ex. 1 + sinA cscA

Page 9: polar plane and - Miss Sahady PSHS Class Websitemisssahadypshsclasswebsite.weebly.com/uploads/5/1/... · 1 January 08, 2014 polar plane and graphing points Ch.8 Lesson 1 Level 1 Simplifying

Level 1 Simplifying Identities Day 1.notebook

9

January 08, 2014

Def: The following trig idenes hold for all values of A, except those for which tangent and cotangent are undefined

Idenes:sin A = tan Acos A 

cos A = cot Asin A

Quoent Idenes:

Page 10: polar plane and - Miss Sahady PSHS Class Websitemisssahadypshsclasswebsite.weebly.com/uploads/5/1/... · 1 January 08, 2014 polar plane and graphing points Ch.8 Lesson 1 Level 1 Simplifying

Level 1 Simplifying Identities Day 1.notebook

10

January 08, 2014

sin2x cot x sec x

Page 11: polar plane and - Miss Sahady PSHS Class Websitemisssahadypshsclasswebsite.weebly.com/uploads/5/1/... · 1 January 08, 2014 polar plane and graphing points Ch.8 Lesson 1 Level 1 Simplifying

Level 1 Simplifying Identities Day 1.notebook

11

January 08, 2014

cotx secx     cscx

Page 12: polar plane and - Miss Sahady PSHS Class Websitemisssahadypshsclasswebsite.weebly.com/uploads/5/1/... · 1 January 08, 2014 polar plane and graphing points Ch.8 Lesson 1 Level 1 Simplifying

Level 1 Simplifying Identities Day 1.notebook

12

January 08, 2014

pythagorean ıdentıtıes

They are:  sin2A + cos2A  = 1sec2A = 1+tan2Acsc2A  = 1+cot2A

Write “Pythagorean” on second flap.  Write the three idenes on  right inside flap

Page 13: polar plane and - Miss Sahady PSHS Class Websitemisssahadypshsclasswebsite.weebly.com/uploads/5/1/... · 1 January 08, 2014 polar plane and graphing points Ch.8 Lesson 1 Level 1 Simplifying

Level 1 Simplifying Identities Day 1.notebook

13

January 08, 2014

Like:  x ( 1‐x ) ==> x – x2

Cosx (secx ‐ cosx) 

Distributing Trig Functions

On Your Own:

tan x ( tan x + cot x) 

Page 14: polar plane and - Miss Sahady PSHS Class Websitemisssahadypshsclasswebsite.weebly.com/uploads/5/1/... · 1 January 08, 2014 polar plane and graphing points Ch.8 Lesson 1 Level 1 Simplifying

Level 1 Simplifying Identities Day 1.notebook

14

January 08, 2014

Foiling Trig FunctionsLike: (1+ x )2 = (1+ x ) (1+x)  

= 12+2x + x2   = 1+2x + x2

Let x = cot A(1+cot A)2 = 

    =

    =

On your own:(cosA + sinA)2

Page 15: polar plane and - Miss Sahady PSHS Class Websitemisssahadypshsclasswebsite.weebly.com/uploads/5/1/... · 1 January 08, 2014 polar plane and graphing points Ch.8 Lesson 1 Level 1 Simplifying

Level 1 Simplifying Identities Day 1.notebook

15

January 08, 2014

Summarizing

TIME!

Page 16: polar plane and - Miss Sahady PSHS Class Websitemisssahadypshsclasswebsite.weebly.com/uploads/5/1/... · 1 January 08, 2014 polar plane and graphing points Ch.8 Lesson 1 Level 1 Simplifying

Level 1 Simplifying Identities Day 1.notebook

16

January 08, 2014

Evaluation:1.

Homework:  Worksheet Day 1 Front and Back

Simplify:  tan2x cos2x cscx