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Inverse Trigonometric Functions Inverse Trigonometric Functions

Inverse Trigonometric Functions - PowerPoint Presentation

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Inverse Trigonometric Functions - PPT Presentation

A bit more practice in Section 47b 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

bounded inverse asymptotes abs inverse bounded abs asymptotes calculator find behavior analysis function continuous symmetry whiteboard domain min max odd func origin

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Slide1

Inverse Trigonometric Functions

A bit more practice in Section 4.7bSlide2

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

x

= –1

No Asymptotes

No End Behavior (bounded domain)Slide3

Analysis 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

–1Slide4

Analysis of the Inverse Tangent Function

D:

R:

Continuous

Increasing

Symmetry: Origin (odd

func

.)

Bounded

No Local

Extrema

Horizontal Asymptotes:

End Behavior:Slide5

Guided Practice

Use a calculator to find the approximate value. Express your

a

nswer in both degrees and radians.

(a)

(b)

(c)Slide6

A note about

composing

trigonometric

and 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:Slide7

Whiteboard

Practice…

Find the exact value without a calculator.

(a)

Evaluate this inverse portion first…

(b)

(c)Slide8

Whiteboard

Practice…

Find the exact value without a calculator.

(d)

(e)