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calandra-battersby | 2016-11-08 | General

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A bit more practice in Section 4.7b. Analysis of the Inverse Sine Function. 1. –1. D:. R:. Continuous. Increasing. Symmetry: Origin (odd . func. .). Bounded. Abs. Max. of at . x. = 1. Abs. Min. of at . ID: 486331

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Slide1

Inverse Trigonometric Functions

A bit more practice in Section 4.7b

Slide2Analysis of the Inverse Sine Function

1

–1

D:

R:

Continuous

Increasing

Symmetry: Origin (odd

func

.)

Bounded

Abs. Max. of at

x

= 1

Abs. Min. of at

x

= –1

No Asymptotes

No End Behavior (bounded domain)

Slide3Analysis of the Inverse Cosine Function

D:

R:

Continuous

Decreasing

Symmetry: About the point

Bounded

Abs. Max. of at

x

= –1

Abs. Min. of at

x

= 1

No Asymptotes

No End Behavior (bounded domain)

1

–1

Slide4Analysis of the Inverse Tangent Function

D:

R:

Continuous

Increasing

Symmetry: Origin (odd

func

.)

Bounded

No Local

Extrema

Horizontal Asymptotes:

End Behavior:

Slide5Guided Practice

Use a calculator to find the approximate value. Express youranswer in both degrees and radians.

(a)

(b)

(c)

Slide6A note about composing trigonometricand inverse trigonometric functions…

The following equations are always true whenever theyare defined:

On the other hand, the following equations are only true for

x

values in the “restricted” domains of sin,

cos

, and tan:

Slide7Whiteboard Practice…

Find the exact value without a calculator.

(a)

Evaluate this inverse portion first…

(b)

(c)

Slide8Whiteboard Practice…

Find the exact value without a calculator.

(d)

(e)

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