solve-the-given-problems-on-a-calculator-find-the-values-of-a-sec-2-10000-and-b-tan-10001-tan-1000-3

Name: solve the given problems on a calculator find the values of a sec 2 10000 and b tan 10001 tan 1000 3
Uploaded: 2021-06-27
Duration: 59 s
Channel: Numerade
Description: Solve the given problems. On a calculator, find the values of (a) $\sec ^{2} 1.0000$ and (b) $(\tan 1.0001-\tan 1.0000) / 0.0001 .$ Compare the values and give the meaning of each in relation to the derivative of tan $x$ where $x=1$

Question

Solve the given problems.
On a calculator, find the values of (a) $\sec ^{2} 1.0000$ and
(b) $(	an 1.0001-	an 1.0000) / 0.0001 .$ Compare the values and give the meaning of each in relation to the derivative of tan $x$ where $x=1$

Carson Merrill · Accepted Answer

First problem, we want to solve the given problem using a calculator. So this is going to be 37. We see, or 39. We have the values of second squared of one. And then we want to look at tangent Of 1.001 Minour Tangent of one, all divided by 0.001. We end up being a very close value to seeking square. And the reason why is because this is uh, for example, what happens when we take a small change and why over a small change in X a small change and why over a small change in X is known as the derivative. So we see that the derivative of the tangent at one is equal to seek and square one.

Tp Sarathy · Answer

okay. We need to solve this equation here to 10. And was X equal. Standing was one over. Forex. So, uh, what makes it a little bit not so straight poetess factor. We have a two facing the 10 in one. Otherwise, people just he quit the on the, um arguments, but the damage was so they need to get out of this to come out. That&#x27;s what we look. And it&#x27;s easy to do if you recognize that to 10 was X is the same as and in physics. Yes. And in worse sex. And in was sick. I mean, up to previous problems. This is equal to and in less X plus X divided by one minus x times X But just and in verse two x divided by one minus Ex quipped. Okay, So the left hand side reduces to 10 in verses because what we want, we got rather, too. It&#x27;s fixing it. Now we have calendars off something equal, standing worse off this thing. So we can just go ahead and take a panna portside. Therefore, what? We have a standing were so because they like, though what we were given s on up next month equals Bannon was were nowhere. Forex. I understand in love. Okay, Now it&#x27;s a matter of simply taking the tangent of both sides and getting out of this town in worse drops out. So what really have a still the arguments that will, you know, we have two x weathered by one minus X squid equals one over for And that said So I&#x27;m gonna cross multiply both sides and the possible to play or the equaled assignments of two x times bullets is eight x where equals one times one minus X squared. Oh, are we? Have what? We have us again and expect to both sides. Nine X squared equals one. Or, in other words, X equals 1/9. Okay, And we have two solutions. X equals less minus one over. That&#x27;s a fun lance. Well, excess one plus minus one of liberty

Ankit Gupta · Answer

according to question, Ben, spread eggs minus off 3 10 X plus one equals zero when experiences your fight. Now, as you can clearly see that this is a quadratic equation. Intendant off fix. So we&#x27;re going to solve. These are we&#x27;re going to find the routes off the secrets and giving our sweethearts. Charlie is rule, so panics. We ve come mind saw minus three less minus off Aguero minus three holes minus four one. What if they say one upon who multiplied? Very one. Police upon quarter simplification. Regulus an X equals three plus minus off through five. Upon to. So from here we&#x27;re doing to get food. Different bills off 10 x and there Dan X equals little point. See, a who&#x27;s it&#x27;ll? Hard panics equals already. You can say approximately will be called who point 61 80 So when Dan it&#x27;s is equal share 0.380 So panics this positive on this positive in the first portrait and deter quarter. So where panics is in cost quadrant, then develop off x will be zip line 36 49 And when panics is in third quadrant, then the value affects with the simply was see point 506 fight. Similarly, when tenants equals 2.6180 in this case also can ixis positive so it will idle lie in first quarter in the third quarter. The Wynn Panics isn&#x27;t for Squadron. Then develop Fix will be simply equals one point who video 59 And when it is in Deter Quadrant, then we can write it as X equals Pi Pless 1.59 So ultimately give us four point three for seven fight. So we&#x27;re getting four different fellas. Affects and there&#x27;s 0.3619 2.5065 1.59 and finally 4.3475 which satisfies is initial equation, for this will be the final answer.

Heather Zimmers · Answer

her part, they were finding the inverse tangent of one. That means we&#x27;re finding the angle whose tangent is one, and the inverse tangent function has arranged of negative pi over to two pi over two. So that means our answer has to fall in that range. And since oneness positive, we&#x27;re going to make a reference triangle in Quadrant one. So one is equivalent to 1/1 if you want to make it into a ratio. So that way we could put one on the opposite and one on the adjacent since Tangent is opposite over adjacent. And once we do that, we realize we have a 45 45 90 triangle. So our reference angle is 45 degrees. And when converted into radiance, that&#x27;s pi Over four for Part B were finding the inverse tangent of negative one. So that&#x27;s the angle whose tangent is negative? One. We&#x27;re still using this range for the inverse tangent function, but this time we&#x27;re going to put our reference triangle in Quadrant four. Since Tangent is negative there, so we have 1/1 as a ratio of opposite over adjacent and again we have a 45 45 90 triangle. So we would describe this angle is negative 45 degrees and in radiance, that would be negative. Pi over four. And for part C, we&#x27;re finding the inverse tangent of zero. Now, when you&#x27;re dealing with zero, you want to think about the unit circle. It&#x27;s a little easier that way. The circle with radius one. So where is the tangent value? Zero. Well, we know that any point on the unit circle has coordinates co sine of the angle sine of the angle, and we know that tangent oven angle is sign over. Co sign. So we&#x27;re looking for where we get zero over something. Okay, so at this point, right here, we have the coordinates 10 So that is zero over something 0/1. And that angle would be zero radiance and zero degrees. So answer for that part is zero

Amit Srivastava · Answer

here we have to calculate the value off the function given by Stange Engulf Dan Degree and Duke or pensioned off 10 degree No, we know that court engine off theta is equals to one upon off tangent titter So instead of contention, Tita, we can write it as one bite pungent data. So we will right here then gentle Ben degree Ah, Born tangent Off turn degree. Here we have written contingent off 10 degree is equal student upon off tangent Pen degree here These will be cancelled out and we have a solution is equal to one so they can right here. Tangent off 10 degree in Tokyo tangent off 10 degree is equals to one

Linh Vu · Answer

attention off the zero. We&#x27;re coaches. Oh, they&#x27;re fund attention in bosoms are also your coaches as well.

Problem

Solve the given problems. Display the graphs of $…

Problem 39 Easy Difficulty

Solve the given problems.
On a calculator, find the values of (a) $\sec ^{2} 1.0000$ and
(b) $(\tan 1.0001-\tan 1.0000) / 0.0001 .$ Compare the values and give the meaning of each in relation to the derivative of tan $x$ where $x=1$

Answer

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

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Basic Technical Mathematics with Calculus

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

Anna Marie V.

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus