find-the-derivatives-of-the-given-functions-on-a-calculator-find-the-values-of-a-1-sqrt1-052-and-b-l

Question

Solve the given problems.
On a calculator, find the values of (a) $1 / \sqrt{1-0.5^{2}}$ and (b) $\left(\sin ^{-1} 0.5001-\sin ^{-1} 0.5000\right) / 0.0001 .$ Compare the values and give the meaning of each in relation to the derivative of $\sin ^{-1} x$ where $x=0.5.$

Stanley Enemuo · Accepted Answer

So we need to find the value of one over the square root of one minus 0.5 squares by using scientific calculator. This gives us 1.154. So we have to hunt the values of part B arc sine of 0.50, warrant mindless oxen of zero point five zero, And that&#x27;s equal to one 154.

James Strickland · Answer

Okay, so today I&#x27;m going to investigate. Funny Arc sine anarchist sign is only defined in the first and fourth quadrants, so Arc sine is only defined in the first quadrants. So its domain is from the beginning of the fourth quadrant, which is negative pie Hafs way down here until I swing around and get the pie halfs. So until pi house And we also know that everything could be defined by the reference angles so focusing on these five major angles in here we can actually find every angle that&#x27;s on the unit circle. And so the baseline Here we call that zero and coming up a little bit. We have pie to the six and then pie to the fore pi to the three and pi over two or by house. And it&#x27;s a sign is all about how high goes weaken. Simply just count up the lines and figure out what values were looking for. In other words, I want to sign of negative one of it&#x27;s a negative one house now, Yes, that negative here. This tells me that&#x27;s in Quadrant four, but since this by reference, I can simply just put a negative Whatever answer I get. And so since the one have some the unit circle, I literally just go up one spot. And so I go up one line and I see my answer is pie six. But again, I want that negative. So I make it negative by six. Likewise, let&#x27;s say I went for sign of its A arc sine of one square root, too. It may not be as clear on this version of what value in talking about, but if I rationalize it if I times square it to, um topping bottom, I get sign arc of square root to over to and again, since my numerator zehr to here at the bottom. I only need to worry about killing up to two, because this trick assumes that everything has a two at the base. So now one to and so this answer here is pie over four, and this is positive. So this is positive. Welcome us. Do one more. Let&#x27;s say we have the arc sine of the negative. Let&#x27;s say square root 3/2. So again we have base to, so we get to use our trick. We&#x27;re in only about our first quadrant and we know we will just make it negative at the end. And so up here we have a three. Yes, we&#x27;re gonna count of three times. One to three. So it&#x27;s the angle that makes this angle right here in that data at that angle we should already memorize is equal to high over three. But because it&#x27;s negative, I need a negative high over three.

Carl David Cepeda · Answer

aren&#x27;t so We have inverse Trigana metric cautions. It will have to about them. So we have first art sign our coastline. We&#x27;re invest call Sign off 1/2. Okay, so, uh, we&#x27;ll have to define first ever interval a pie So that say our better here or our solution here will be from 0 to 2 pi. All right, so we only have one solution for each. Uh hey, now. Ah, the art sign our Arkle sign off 1/2. Yes, actually, the inverse off. Cool sign. See, then, uh, just quotes one. So we&#x27;re have to look for the value of Ceta and through the unit circle. Hey, Ferre is actually by over. Three paints are going to live in the circle. Their eyes you got to buy over. Okay, so that is the co sign off by Over. The is equal to 1/2. Right. Next we are to get the our coastline off. Native won over squared. Okay, so first we have to rationalise averaging on meter. So we have Marco sign off. Netted one prescribed to let&#x27;s multiply the new were either in the number of my square to this is Are you sign off negative skirt of to over to Hey, so we are to get it&#x27;s bound. That is the cool sign off tape, huh? Better. It&#x27;s negative spirit of to. Over. Okay. And in the unit circle, we know that the co sign off three pie over four. It&#x27;s actually negative spirit of two over. Therefore, this is people to three. High mover for hay. So you just look it up on leaving it circle. Right? Finally, we have our co sign off spirit of three over. So the denominator for has been rationalized and we know that who signed by over sits ISS actually off described three over to in the circle. Therefore, this is supported by over six. Yeah.

Carl David Cepeda · Answer

All right. So for this problem, we have to define first Albert Turbo. So let&#x27;s say that our value. Why ISS off the finger sign off X s in the interval. Negatives. Uh, pi over two. Too high. Hey. So that&#x27;s about a whipped first art sign or sine inverse off. Negative one. Okay, so we know that, uh, sign off. Negative by two. That is on the search is on the box on the over part of our Y axis. Okay? And the years of hell, this people to negative one. Therefore, since this is a response Shin, then our answer to sneak up there. Hi. Over. Okay. And then for letter, you we have exciting or citing grace. Negative. Long over squared of tea. Hey, rationalizing the anomaly for you have inverse of sign off. Negative squared off to over to okay. And we know in the in circle that sign up negative by over four. It&#x27;s actually negative. Skirt of to over to therefore the answer for letter A. It&#x27;s negative by over for All right,

James Strickland · Answer

today, I&#x27;m going to investigate calculating our co sign our co sign. It&#x27;s bounded between the first and second quadrants here. So it&#x27;s only gonna exist in Cuba on work You two. And we know that everything&#x27;s relatable to the first quadrant by reference angle. So more specifically, I&#x27;m only going to focus on this one quadrant and then just decide if I need to reflect it across to the second quadrant as necessary. And so I have these five major angles in the first quadrant that we&#x27;re focusing in on with the one appear Being High Hafs. Then we have high thirds Hi Force Pie six and then finally zero. And coastline, of course, is related to X, and it&#x27;s all about how far out it goes. So they&#x27;re straight up line here is directly above the origin, so it&#x27;s a zero distance out, and then we have a one. Everything is, of course, in a factor of two form, and so now we&#x27;re out of distance of two because it&#x27;s the second line. 12 then the third line here. Swear it 3/2 and find the four flying, which is squared for over two. What&#x27;s reduces to one. So using these values, we can then find the art co sign and as we know are co sign is given an angle when you&#x27;re in putting in a measurement. So if I want, for example, the Art Co. Sign of zero, I&#x27;m referring to the zero of the measurement, and I want to know the angle that makes that so this is simply pi over two. Likewise, if I want the angle, let&#x27;s say our co sign of negative one well, by reference, I see the positive one is on this axis, and so I just need to reflect it across to the other sides of among this side, and I want to reflect it across all the way to the other side, referring to the whole angle all the way across. It&#x27;s at this angle, then becomes just pie, since half ways pie has the whole way. All the way across is just pie. So that&#x27;s two examples investigating off our coast

Shaza Hammoud · Answer

and it&#x27;s a question it&#x27;s required to find the exact solution off the following equation. So we have the in both sides of the equation. We have the M recile X, and we have numbers, which are my stoop Iron Man three pie. So the first thing is to solve for the inverse N of X and other was we want to isolate the Anderson off X and one side on other things in the other side. Other things, I mean constant numbers. So let&#x27;s shifty tooth and recitals X to the other side by subtracting to the every sign off X from both water size off the equation for So this will be cancelled with this by subtracting minus to D to sign every sign of X from and here five in recite off X minus two sides Recite off X. This leads toe three is at it as if it is five. X minds to x will be three x five miles stool, be three. So we will get Here&#x27;s three every sign. Oh, fakes minus two pi remain the same. And here in the other side we have with my three by the second step is to take the minds to part with the other side. This can be done by adding to buy tow both sides off the equation. So this will be counseled with this on. Now we get three every sign off X equals toe minus three by plus to buy it, just as my three plus two will be mice one. So it&#x27;s mice one pie minus five. Now let&#x27;s divide by three for both sides of the equation to get rid off the coefficient with the three as Dick option Where the every sign off X as I want eyes without the person off X alone in the left hand side of the equation. So three will be castled here and now I get the Empress Sign off. X equals two minus by over four white off three. Now, as you can see, this is in the form off the Why invest requests in recent off X. So here is the Y, and it&#x27;s equals two and percent of X, which can be written as deform off X equals to sign off. Why? So we can I as X equals to sign off minus pi over three. So this is X it was so sign minus by over three, which is known to be mined stuff. So that&#x27;s it. Off solution off this equation in just one solution, which is minds half.

Problem

Solve the given problems. Display the graphs of $…

Problem 35 Easy Difficulty

Solve the given problems.
On a calculator, find the values of (a) $1 / \sqrt{1-0.5^{2}}$ and (b) $\left(\sin ^{-1} 0.5001-\sin ^{-1} 0.5000\right) / 0.0001 .$ Compare the values and give the meaning of each in relation to the derivative of $\sin ^{-1} x$ where $x=0.5.$

Answer

Related Courses

Basic Technical Mathematics with Calculus

Related Topics

Discussion

Top Calculus 1 / AB Educators

Catherine R.

Heather Z.

Kayleah T.

Kristen K.

Calculus 1 / AB Courses

Precalculus Review - Intro

Functions on the Real Line - Overview

Recommended Videos

Watch More Solved Questions in Chapter 27

Video Transcript

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

Catherine R.

Heather Z.

Kayleah T.

Kristen K.

Precalculus Review - Intro

Functions on the Real Line - Overview

What do you need help with?

Textbooks

Ask a question

Courses

AI Tutor

Basic Technical Mathematics with Calculus

Catherine R.

Heather Z.

Kayleah T.

Kristen K.

Precalculus Review - Intro

Functions on the Real Line - Overview

Allyn J. Washington, Richard S. EvansBasic Technical Mathematics with Calculus

Catherine R.

Heather Z.

Kayleah T.

Kristen K.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus