find-an-equation-of-the-tangent-line-to-the-curve-at-the-given-point-ysin-sin-x-quadpi-0

Question

Find an equation of the tangent line to the curve at the
given point.
$y=\sin (\sin x), \quad(\pi, 0)$

Amrita Bhasin · Accepted Answer

this question gives us why is sign of sign of acts and the point pie Comma zero. First step is we need to find the derivative because the gold this question is to find the equation of the tangent. We need to find the derivative first. Okay, we know the derivative of Sign is co sign and then we know, but we maintain the sign of acts. So instead of sign of sign of X, the derivative of Sinus co sign of sign of axe and then the derivative of sign is cosign of ex again. So this simplifies are derivative to be co sign of acts Times Co Sign of sign of axe. Okay, now we have the point pie comma zero. Therefore, plug in pie. There&#x27;s some plus two negative one time to plug into point slope form. Given the point, Pikom a zero. Why? I&#x27;m honest hero is negative one, which was our m. We just figured us out in the previous slide. This simplifies to express wise pie

Maurizia De Palma · Answer

So the question asked us to find the tangent line of why equal sign of X when X equals zero on their three steps when we&#x27;re solving questions like this. So Step number one is going to be to find that the derivative of your function and our function that we were given was Why equals Sign of X and the derivative of Sign is co sign of X. Step two is then to plug the X value into your derivative into terrific into derivative. Great. So we had why a prime equal co sign of X and now we have y of prime equals co sign of zero, right? That&#x27;s what they gave us. And again, this is where the unit circle is going to come in handy. So one remember zero is this point here and has the value of one comma zero and our coastline is always our X value. So we plug it in, we get why prime equals one, and their last step is now to write our equation. And there&#x27;s a special formula that we have to follow here. And that is why I minus f of a a being that the term they gave us. So here we have X equals zero equals f prime of A, which is a derivative that we found in step two. Step two times X minus a Again a is X equals zero. So now we just plug in the terms. So we have why minus zero equals one times X minus zero and we have to distribute this one to both terms. So our final answer is why equals X?

Clarissa Noh · Answer

it&#x27;s layers of a new married here. So we have y is equal to co sign checks minus sign. Thanks. Sure, if it is gives us negative sign minus co sign. So we&#x27;re gonna plug in Xs equal to pi, which gives us two slope of detention. This gives us one. So using the point slope formula, we get wine minus negative. One over X minus pi was equal to one. So I get why is equal to us minus pi minus one.

Nicholas Barvinok · Answer

we have the function, Why equals sine X plus sign Square X and we want to find the equation of the tangent line to that function at the 0.0 Now the first thing we should check is that 00 is actually a point on the graph of dysfunction. By plugging X equals zero, I get sign of zero, which is zero plus sine squared of zero, which is zero times 00 So I get zero and the 00.0 is indeed on the graph of this of this function. So that&#x27;s good. So we want the equation of the tent of some tangent line to find the equation of a line in general, it is sufficient to know the slope of the line and a point on the line so that we can then used this standard formula for the equation of a line. Why, minus y one equals and the times x minus X one where X one y one is a point on our line and em is the slope. Well, we already have a point on our line. The tangent line to this function at 00 passes through 00 So we have a point on our line. The only thing we need to find is M the slope of our tangent line and the slope of our tangent line at 00 will be the derivative of this function at X equals zero. So what we should do next is take the derivative of dysfunction. So the derivative of Sine X is co sign X. And now we use the chain rule. We have an inter function sign of X and an outer function and input raised to the power of two by the chain rule. We start with taking the derivative of the outermost layer, which is an input squared. Take the derivative of that by the power we bring the two down, keep the input the same and subtract one from the original exponents that becomes exponents of one and then multiply by the derivative of the input. The inter function sign of X. The derivative of that is co sign next and this is a one in fact, not a prime. So here&#x27;s our why Prime, We can now plug in zero to get the slope of the tangent line at that point co sign of zero is one plus two times sign of zero is zero and then times one. So this term is zero. So this whole thing equals once our slope is one. So now we just plug in the relevant data into our equation, and it simplifies to y equals X, and that&#x27;s it.

Clarissa Noh · Answer

it&#x27;s clear. So when you read here, so you have why is equal to X? Less tension in the slope. Get one plus seeking square When we were gonna plug in excess equal to pi to get our slope we get to so using the point slope formula You know why minus pi over It&#x27;s minus by which is equal to two way simplifying we get why is equal to two x minus pi?

Clarissa Noh · Answer

Hey, it&#x27;s clear sailing right here. So we have Why this people to sign next? Less coastline X. So the door. If it is well equal, co sign X minus sign X. It&#x27;s slow if we plug in zero, we get one and find me. We just plug it in. We get one for being your line is why, if equal to X plus one.

Problem

Find an equation of the tangent line to the curve…

Problem 43 Hard Difficulty

Find an equation of the tangent line to the curve at the
given point.
$y=\sin (\sin x), \quad(\pi, 0)$

Answer

$x+y=\pi$

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Video Transcript

James Stewart

Biocalculus Calculus for the Life Sciences

Grace H.

Catherine R.

Anna Marie V.

Michael J.

Precalculus Review - Intro

Functions on the Real Line - Overview

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$x+y=\pi$

Biocalculus Calculus for the Life Sciences

Grace H.

Catherine R.

Anna Marie V.

Michael J.

Precalculus Review - Intro

Functions on the Real Line - Overview

James StewartBiocalculus Calculus for the Life Sciences

Grace H.

Catherine R.

Anna Marie V.

Michael J.

James Stewart

Biocalculus Calculus for the Life Sciences