Need Help Solving This Math Problem?

[c00ky]

A Math Problem...

Hi Guys,

I'm totally stuck on the following problem, if anybody could spare me some of their time to guide me through the solution that would be great.

I have a screenshot of the problem on the following site...

http://putfile.com/pic.php?pic=main/8/22412435578.jpg&s=f10"

 

[0rthodontist]

Step 1 is expand the series to 4 terms. Do you know what the 0th term is?

 

[c00ky]

This is what i have so far:

http://putfile.com/pic.php?pic=main/8/22414282061.jpg&s=f10

This (i think) is the 4 terms.

I do not know what to do after this

 

[0rthodontist]

That looks correct. The one comment I have is that it is not legitimate to expand it like that, using all r's. If you use r in an expression, then wherever else the r appears in the expression, it has to mean the same thing--you can't have one group of r's be 0, the next be 1, and so on. You should just skip straight to the step where you substitute in the values.

The next step is to check to see that it approximates the cosine. Calculate the cosine of some angle t and then evaluate that series of 4 terms where x = t.

 

[c00ky]

"The next step is to check to see that it approximates the cosine. Calculate the cosine of some angle t and then evaluate that series of 4 terms where x = t."

How do I do this? This is the part I am unsure about.

 

[0rthodontist]

let's say I have a series of 4 terms, x + x^2 + x^3 + 5x^4
Now if I want to evaluate this series at x = 2, this is what I do:
2 + 2^2 + 2^3 + 5*2^4
= 2 + 4 + 8 + 160
= 174

You want to do a similar thing, but with an angle in radians.

 

[c00ky]

I'm trying but I'm not understanding what I should be seeing at the end of my calculations.

 

[0rthodontist]

Well, what are your calculations?

 

[c00ky]

X = 5

substitue:

= 1 - (1/2x5^2) + (1/24x5^4) - (1/720x5^6)

= 1 - 12.5 + 26.041666... - 21.7013888...

= - 7.159722

What does this mean? (My maths teacher was a Media teacher)

 

[0rthodontist]

What that means is that using the approximation of the first four terms of the series, cos 5 = -7.16. This is clearly not true, but remember that it's only an approximation: it can be wrong. In fact the error increases as the absolute value of x increases. Try a smaller x, say x = 1, instead.

 

[c00ky]

X = 1

substitue:

= 1 - (1/2x1^2) + (1/24x1^4) - (1/720x1^6)


= 1 - (0.5) + (0.041666..) - (0.0013888...)

= 0.5402778

?

 

[0rthodontist]

Now what's cos 1?

 

[c00ky]

0.999847695

 

[c00ky]

I think i had my calculator set in the wrong mode...

I switched it to 'RAD'

and it came up

0.5403

 

[Robokapp]

This is what i have so far:

http://putfile.com/pic.php?pic=main/8/22414282061.jpg&s=f10

This (i think) is the 4 terms.

I do not know what to do after this

I have to ask, how did you do step one? all I see is copying it 4 times.