• Support PF! Buy your school textbooks, materials and every day products via PF Here!

Determine the lenght of arc and the area of the sector subtended by an

  • Thread starter luigihs
  • Start date
86
0
Determine the lenght of arc and the area of the sector subtended by an angle of 60° in circle of radius 3 m

Ok First change 60to radian measure. 60 x pi / 180° = 2pi / 6

Then.. I used the formula s = rθ 3(2pi/6) = 6pi/6 = pi <--- Is this right??

And how can I find the area which formula can I use?
 
407
0
Re: Trigonometric

You could just have kept the angle in degrees and worked out the arc length by using,

[itex]\ c=pi*d[/itex]

and then multiplied that answer by,

[itex]\frac{60}{360}[/itex]
 
86
0
Re: Trigonometric

You could just have kept the angle in degrees and worked out the arc length by using,

[itex]\ c=pi*d[/itex]

and then multiplied that answer by,

[itex]\frac{60}{360}[/itex]
Ok but my answer is right?
 
407
0
Re: Trigonometric

Yes your answer is correct.

That might give you a clue how to find the area of the sector. Think of the fraction of the total circles area you are looking for?
 
86
0
Re: Trigonometric

Yes your answer is correct.

That might give you a clue how to find the area of the sector. Think of the fraction of the total circles area you are looking for?
A = 60 / 360 x 2 ∏ 3 ??
 
407
0
Re: Trigonometric

A = 60 / 360 x 2 ∏ 3 ??
Nearly. You're along the right lines but your calculation for the total area is wrong, [itex]\ a = pi * r^{2}[/itex]

So for the sector area your equation should be,

[itex] Area of Sector = \pi r ^ {2} * \frac{Angle of Sector°}{360°}[/itex]
 
Last edited:
86
0
Re: Trigonometric

Nearly. You're along the right lines but your calculation for the total area is wrong, [itex]\ a = pi * r^{2}[/itex]

So for the sector area your equation should be,

[itex]\ Area of Sector = ( pi * r ^ {2} )* (\frac{Angle of sector°}{360°})[/itex]
Ok so A = 9 pi x 60 / 360 = 540 pi / 360 = 3pi / 2
 
86
0
Re: Trigonometric

Yay!! Hey do you know how to determine cos or sin without calculator?? like cos 75° any hint?
 
407
0
Re: Trigonometric

Yay!! Hey do you know how to determine cos or sin without calculator?? like cos 75° any hint?
I found this on another website.

For sin(x)

[itex] x - \frac{x^ {3}}{3!} + \frac{x^ {5}}{5!} -\frac{x^ {7}}{7!} + ...[/itex]

For cos(x)

[itex] 1 - \frac{x^ {2}}{2!} + \frac{x^ {4}}{4!} -\frac{x^ {6}}{6!} +...[/itex]

From a bit of quick testing here these series seem to converge to the right value fairly quickly.

Not sure if that really helps you much

AL
 
407
0
Re: Trigonometric

Also I forgot to say that you need to be using radian values for those 2 series to work.

edit.

I just realized you would still need a basic calculator to do that.

Without a calculator of any sort your options are really either getting a trig table sheet or learning some of the common ones like 0, 30, 45, 60, 90 etc
 
Last edited:
32,620
4,354
Re: Trigonometric

I found this on another website.

For sin(x)

[itex] x - \frac{x^ {3}}{3!} + \frac{x^ {5}}{5!} -\frac{x^ {7}}{7!} + ...[/itex]

For cos(x)

[itex] 1 - \frac{x^ {2}}{2!} + \frac{x^ {4}}{4!} -\frac{x^ {6}}{6!} +...[/itex]
These are the Maclaurin series for the sine and cosine functions. Maclaurin series are special cases of Taylor series.
From a bit of quick testing here these series seem to converge to the right value fairly quickly.

Not sure if that really helps you much

AL
 
407
0
Re: Trigonometric

These are the Maclaurin series for the sine and cosine functions. Maclaurin series are special cases of Taylor series.
Thanks Mark, I haven't really studied series in school in much detail yet so thanks for telling me what those where.

Thanks
AL
 

Related Threads for: Determine the lenght of arc and the area of the sector subtended by an

  • Posted
Replies
1
Views
666
  • Posted
Replies
11
Views
2K
Replies
5
Views
2K
  • Posted
Replies
7
Views
4K
  • Posted
Replies
7
Views
725
  • Posted
Replies
7
Views
974
Replies
11
Views
690

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving

Hot Threads

Top