The $4^{ ext {th }}$ degree Taylor polynomial for $\sin (x)$ centered at $a=\frac{\pi}{6}$ is given by the following.

$
\sin (x)=\frac{1}{2}+\frac{\sqrt{3}}{2}\left(x-\frac{\pi}{6} ight)-\frac{1}{4}\left(x-\frac{\pi}{6} ight)^{2}-\frac{\sqrt{3}}{12}\left(x-\frac{\pi}{6} ight)^{3}+\frac{1}{48}\left(x-\frac{\pi}{6} ight)^{4}+R_{4}(x)
$

Using this, estimate $\sin \left(40^{\circ} ight)$ correct to five decimal places.

Question

The $4^{	ext {th }}$ degree Taylor polynomial for $\sin (x)$ centered at $a=\frac{\pi}{6}$ is given by the following.

$
\sin (x)=\frac{1}{2}+\frac{\sqrt{3}}{2}\left(x-\frac{\pi}{6}ight)-\frac{1}{4}\left(x-\frac{\pi}{6}ight)^{2}-\frac{\sqrt{3}}{12}\left(x-\frac{\pi}{6}ight)^{3}+\frac{1}{48}\left(x-\frac{\pi}{6}ight)^{4}+R_{4}(x)
$

Using this, estimate $\sin \left(40^{\circ}ight)$ correct to five decimal places.

StudyXY · Accepted Answer

: Convert the given angle from degrees to radians. : Substitute the given value into the Taylor polynomial. : Calculate the approximate value. : Round the result to five decimal places. The estimated value of $\sin \left(40^{\circ}\right)$ correct to five decimal places is approximately $0.64279$.

Q
QuestionAnatomy and Physiology

Answer

Full Solution Locked

Step 1
: Convert the given angle from degrees to radians.

Step 2
: Substitute the given value into the Taylor polynomial.

Final Answer

Need Help with Homework?

Related Questions

Company

Explore

Study Tools

QQuestionAnatomy and Physiology

AnswerHelpful