Warm-up!

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Warm-up!

1. State the domain and range of the relation
   (-2,4), (1,3), (-2,-2).
   Is the relation a
   function?
2. Find f?g(x) and g?f(x) for
   f(x) 2x 4 and g(x) x2
3. Write the equation in slope-intercept form for
   the line with a slope of 6 and passing through
   the point (-3,4).
4. Graph f(x) 4 x
5. Graph 2x y lt 7

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Welcome to Unit 8! Chapter 7 Hat Trig!

• In this unit we will learn
• 8.1 simplify trigonometric expressions (7-1)
• 8.2 verify trigonometric equations (7-2)
• 8.3 use sum and difference identities to solve
  problems (7-3)
• 8.4 use half and double angle identities to
  solve problems (7-4)
• 8.5 solve trigonometric equations (7-5)

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8.1 simplify trigonometric expressions (7-1)

• In this section we will answer
• Just what is a trig identity?
• What are the basic trig identities?
• How can I use them to simplify expressions?

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What is a trig identity?

• A trig identity is an equality between two trig
  expressions which is true for ALL values of the
  variable.
• To disprove an identity all you have to do is
  find one value that does not work in the
  equality.

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What are the basic trig identities?

• Many of these you already know or can easily
  find!

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Remember these?
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The Quotient Identities
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Simplify
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Pythagorean Identities
r
y
x
Lets build them from scratch!
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Are these the same?
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Let us try to simplify!
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Let us try to simplify!
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Let us try to simplify!
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Let us try to simplify!
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Using Identities to find trig values

• Choose an identity which uses both tangent and
  secant.
• Substitute for tan x.
• Solve for secant.
• Determine the sign needed by the quadrant.
• Could also be found using a right triangle and
  Pythagorean theorem.

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Using Identities to find trig values
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Homework and Upcoming Events

• p 427 19 35 and 39 53 odd
• Reassessments due Wednesday!

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Warm-up

• p A38 Lesson 7-1 all

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Homework
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8.2 verify trig equations (7-2)

• In this section we will answer
• Are there more identities possible?
• How can I be sure that an identity is really true
  without trying every angle on earth?
• Can I use identities to find actual answers to
  problems?

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Are there more identities possible?

• There are an any number of identities possible.
• As long as you build them based on existing
  identities you can make them all day!

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How can I be sure that an identity is really true
without trying every angle on earth?

• Algebraic Manipulation and Basic Trig Identities
• The Dos
• DO simplify the more complicated side.
• DO substitute (a lot!) using Basic Trig Ids.
• DO factor if possible.
• DO multiply numerators and denominators by the
  same trig function.
• DO find common denominators when you can.
• The Donts
• DONT work both sides of the equation at once!
• If you want to switch, STOP working that side and
  move to the other.
• DONT move anything from one side to the other!

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Lets try one! Verify the following id.
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Verify the following identity.
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Verify the following identity.
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Can I use identities to find actual answers to
problems?

• Sure can! Watch!
• Goal! Get one trig function a number

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Another

• Find a numerical value of one trigonometric
  function of x.

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A couple word problems

• p 435 40 and 42

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Homework and Upcoming Events

• p 434 13 39 odd and 43
• Quiz on tomorrow!
• Unit 8 Test after break.

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Warm-up
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Homework
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Section 7-3 Sum and Difference Identities

• In this section we will answer
• How can I manipulate an expression using trig
  identities so that I can solve it without a
  calculator?

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Our handy-dandy handout!
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Homework

• p 442 15 39 odd 43
• Unit 8 Test after the break!

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Warm-up

• Flashcards!

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Homework
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Section 7-4 Double Angle and Half Angle
Identities

• In this section we will answer
• What other methods do I have to find trig ratios
  without a calculator?

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Question Does ?
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DOUBLE ANGLE Ids

• If ? represents the measure of an angle, then the
  following identities hold for all values of ?

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ex. If , and the angle is in the
first quadrant, find the exact value of the
following
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If ? represents the measure of an angle, then
the following identities hold for all values of
?
Choose or based on _________________________
__
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ex. Find an exact value for sin 195?.
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ex. Verify
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Homework

• p 454 15-35 odd and 38
• Test for Unit 8 Tuesday
• FINAL
• Open-Ended on Friday, June 13th
• Multiple Choice on Tuesday, June 17th

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Warm-up

• A38 Lesson 7-4 all
• Get your homework out!

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Homework
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Section 6-8 and 7-5 Solving Trig Equations

• In these sections we will answer
• How can I use trig ratios and trig
  identities to solve equations?

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Principle Values

• Can generate a positive or a negative angle for a
  given trig ratio.
• Uses the first quad and an adjacent quad.
• Your calculator works in principle values.
• Designated by a capital letter

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Which Quads?
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Start simpleDo odds in degrees/evens in radians
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Let's step it up!
Solve the equation for the principal values of x.
Express your
solutions in degrees.
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Solve the equation for the principal values of x.
Express your
solutions in degrees.
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Solve the equation
for all values of ? from 0 ? lt 2p
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Solve the equation for the principal values of y
in degrees.
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Solve the equation for all real values of ß in
radians.
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Solving by graphing
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Partner Work

• One piece of paper per partnership.
• Partners will work together to write the first
  problem.
• After that, one person solves, the other
  coaches/praises then switch.
• Only one person at a time is working.
• P459 4 14 all

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Homework

• P459 17 47 odd, 57 and 58
• Test Wednesday!!!
• 7-1 to 7-5