February 6, 2012At the end of today, you will be able to understand inverse trig functions.

Warm-up: Trig Review without a calculator.

1. 2. 3.

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cosπ

4

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sin −π

6

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tan −π

4

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⎠ ⎟

Lesson 4.7 Inverse Trig FunctionsDefinitions of the Inverse Trigonometric Functions

• y = arcsin x if and only if sin y = x- Domain -1 ≤ x ≤ 1; Range

• y = acrcos x if and only if cos y = x - Domain -1 ≤ x ≤ 1; Range 0 ≤ y ≤ π

• y = arctan x if and only if tan y = x - Domain -∞ < x ∞; Range

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−π2

≤ y ≤π

2

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−π2

≤ y ≤π

2

Tomato, tomahto?Same thing!

Example 1: Find the exact value for each:Keep the range in mind for each function!a) b) c)

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arcsin x( ), sin−1 x( )?

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arcsin −1

2

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cos−1 2

2

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arctan −1( )

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=−π6

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=π4

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=−π4

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Range : −π

2≤ y ≤

π

2

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Range : −π

2≤ y ≤

π

2Range 0 ≤ y ≤ π

Evaluating Compositions of Functions

Example 2: Find the exact value.

Practice:1. 2.

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tan arccos2

3

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⎠ ⎟Work from the inside out.

Use right triangle trigonometry to find the missing leg.

u

2

3

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tan u( ) =opp

adj

√5

Let u = arccos 2/3

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=5

2

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cos arcsin−3

5

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sin arcsin3

4

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Practice Together

Evaluate the expression Use a right triangle to helpwithout using a calculator. evaluate the expression.1. arcsin 0 5. 2. arccos 03. 6.

4.

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sin−1 −2

2

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tan−1 3

3

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sec arcsin4

5

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sin tan−1 x( )

HW 4.7Pg. 349 #1-15odd, 49-61 odd

1. 15. 61.3. 49. 5. 51.7. 53.9. 55.11. 57.13. 59.

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arcsin1

2

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arccos1

2

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arctan3

3

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cos−1 −3

2

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arctan − 3( )

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arccos −1

2

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sin−1 3

2

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tan−1 0

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sin arctan3

4

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cos tan−1 2( )

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sec arctan −3

5

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cos arcsin5

13

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sin arccos −2

3

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cot arctan x( )

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cos arcsin2x( )

Valentine’s Extra CreditHeart on Graphing Calculator

Draw a heart on your graphing calculator that will make the bottom at the origin.

Give me the equation/s you typed in and show your work to get full credit.