polar plane and - miss sahady pshs class...
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Level 1 Simplifying Identities Day 1.notebook
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January 08, 2014
polar plane and graphing points
Ch.8 Lesson 1
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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
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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
Level 1 Simplifying Identities Day 1.notebook
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trıg expressıonsDef: ‐trig funcons, variables and constants
put together without an equal sign
Ex. cosx – x
sin2 a + cos2a
1‐sec B tanB
Level 1 Simplifying Identities Day 1.notebook
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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
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Wha
t are
we
goin
g
to u
se to
do
this
?
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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
Level 1 Simplifying Identities Day 1.notebook
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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
Level 1 Simplifying Identities Day 1.notebook
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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:
Level 1 Simplifying Identities Day 1.notebook
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sin2x cot x sec x
Level 1 Simplifying Identities Day 1.notebook
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January 08, 2014
cotx secx cscx
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pythagorean ıdentıtıes
They are: sin2A + cos2A = 1sec2A = 1+tan2Acsc2A = 1+cot2A
Write “Pythagorean” on second flap. Write the three idenes on right inside flap
Level 1 Simplifying Identities Day 1.notebook
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Like: x ( 1‐x ) ==> x – x2
Cosx (secx ‐ cosx)
Distributing Trig Functions
On Your Own:
tan x ( tan x + cot x)
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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
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Summarizing
TIME!
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Evaluation:1.
Homework: Worksheet Day 1 Front and Back
Simplify: tan2x cos2x cscx