View by Category

The presentation will start after a short

(15 second) video ad from one of our sponsors.

Hot tip: Video ads won’t appear to registered users who are logged in. And it’s free to register and free to log in!

(15 second) video ad from one of our sponsors.

Hot tip: Video ads won’t appear to registered users who are logged in. And it’s free to register and free to log in!

Loading...

PPT – Inverse Trig Functions and Differentiation PowerPoint presentation | free to download

The Adobe Flash plugin is needed to view this content

About This Presentation

Write a Comment

User Comments (0)

Transcript and Presenter's Notes

Inverse Trig Functions and Differentiation

- By
- Dr. Julia Arnold

Since a function must pass the horizontal line

test to have an inverse function, the trig

functions, being periodic, have to have their

domains restricted in order to pass the

horizontal line test. For example Lets look at

the graph of sin x on -2pi, 2 pi.

Flunks the horizontal line test.

By restricting the domain from - pi/2, pi/2 we

produce a portion of the sine function which will

pass the horizontal line test and go from -1,1.

The inverse sine function is written as y

arcsin(x) which means that sin(y)x. Thus y is an

angle and x is a number.

Y sinx

Y arcsin x

We must now do this for each of the other trig

functions

Y cos x on 0, pi Range -1,1

Y arccos (x) on -1,1 range 0, pi

arctan(x) has a range of (- pi/2,

pi/2) arccot(x) has a range of (0,

pi) arcsec(x) has a range of 0, pi, y

pi/2 arccsc(x) has a range of - pi/2, pi/2,

y 0

Evaluate without a calculator

Step 1 Set equal to x

Step 2 Rewrite as

Step 3 Since the inverse is only defined in

quadrants 1 4 for sin we are looking for an

angle in the 4th quadrant whose value is -1/2.

The value must be - pi/6.

Evaluate without a calculator

Step 1 Set equal to x

Step 2 Rewrite as

Step 3 The inverse is only defined in quadrants

1 2 for cos so we are looking for the angle

whose value is 0.

The value must be pi/2.

Evaluate without a calculator

Step 3 The inverse is only defined in quadrants

1 4 for tan so we are looking for the angle

whose tan value is sqr(3).

The tan 60 sqr(3) or x pi/3

Evaluate with a calculator

Check the mode setting on your calculator.

Radian should be highlighted. Press 2nd function

sin .3 ) Enter. The answer is .3046

Inverse Properties

If -1 lt x lt 1 and - pi/2 lt y lt pi/2 then

sin(arcsin x)x and arcsin(siny)y

If - pi/2 lt y lt pi/2 then tan(arctan x)x and

arctan(tany)y

If -1 lt x lt 1 and 0 lt y lt pi/2 or pi/2 lt y lt pi

then sec(arcsec x)x and arcsec(secy)y

On the next slide we will see how these

properties are applied

Inverse Properties Examples

Solve for x

If - pi/2 lt y lt pi/2 then tan(arctan x)x and

arctan(tany)y

Thus

Inverse Properties Examples

If

where 0 lt y lt pi/2 find cos y

Solution For this problem we use the right

triangle

Sin(y) x, thus the opp side must be x and the

hyp must be 1, so sin y x

1

x

By the pythagorean theorem, this makes the bottom

side

Cos(y)

Inverse Properties Examples

find tan y

If

Solution For this problem we use the right

triangle

By the pythagorean theorem, this makes the opp

side

1

2

tan(y)

Derivatives of the Inverse Trig Functions

Examples Using the Derivatives of the Inverse

Trig Functions

Note u du/dx

Find the derivative of arcsin 2x

Let u 2x du/dx 2

Examples Using the Derivatives of the Inverse

Trig Functions

Note u du/dx

Find the derivative of arctan 3x

Let u 3x du/dx 3

Examples Using the Derivatives of the Inverse

Trig Functions

Find the derivative of

Let

Some more examples

Let

find

Solution Use the right triangle on the

coordinate graph

Now using the triangle we can find sec x after

we find the hyp.

Some more examples

Write the expression in algebraic form

Let then

Solution Use the right triangle

Now using the triangle we can find the hyp.

3x

y

1

Some more examples

Find the derivative of

Let u

Please let us know if this presentation has been

beneficial. Thanks.

About PowerShow.com

PowerShow.com is a leading presentation/slideshow sharing website. Whether your application is business, how-to, education, medicine, school, church, sales, marketing, online training or just for fun, PowerShow.com is a great resource. And, best of all, most of its cool features are free and easy to use.

You can use PowerShow.com to find and download example online PowerPoint ppt presentations on just about any topic you can imagine so you can learn how to improve your own slides and presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

You can use PowerShow.com to find and download example online PowerPoint ppt presentations on just about any topic you can imagine so you can learn how to improve your own slides and presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

Recommended

«

/ »

Page of

«

/ »

Promoted Presentations

Related Presentations

Page of

Page of

CrystalGraphics Sales Tel: (800) 394-0700 x 1 or Send an email

Home About Us Terms and Conditions Privacy Policy Contact Us Send Us Feedback

Copyright 2015 CrystalGraphics, Inc. — All rights Reserved. PowerShow.com is a trademark of CrystalGraphics, Inc.

Copyright 2015 CrystalGraphics, Inc. — All rights Reserved. PowerShow.com is a trademark of CrystalGraphics, Inc.

The PowerPoint PPT presentation: "Inverse Trig Functions and Differentiation" is the property of its rightful owner.

Do you have PowerPoint slides to share? If so, share your PPT presentation slides online with PowerShow.com. It's FREE!

Committed to assisting Tcc University and other schools with their online training by sharing educational presentations for free