Length of arc and area of a sector (1 Viewer)

[BlueGas]

I just need some clarifying on this. When you are given the angle in degrees, do you have to convert the degree into radians?

 

[enigma_1]

Yeah

 

[swagswagyoloswag]

Yes, you convert it to radians in order to use the arc length and area of a sector formula

 

[BlueGas]

Yeah

Yes, you convert it to radians in order to use the arc length and area of a sector formula

Thanks you lads.

 

[BlueGas]

Didn't want to create a separate thread for this question so I'm posting it here.

The radius of the earth is 6341km, what arc length would be subtended by an angle of 1 minute at the earth's centre?

 

[InteGrand]

Didn't want to create a separate thread for this question so I'm posting it here.

The radius of the earth is 6341km, what arc length would be subtended by an angle of 1 minute at the earth's centre?

1 minute is 1/60 of a degree.

So the required arc length is (correct to 4 sig. fig.).

(Using arc length = angle/(360 degrees) × 2πR)

 

[BlueGas]

1 minute is 1/60 of a degree.

So the required arc length is (correct to 4 sig. fig.).

(Using arc length = angle/(360 degrees) × 2πR)

Okay, so you used 360, how about if I was to use 180? What would I use? 180/Pi? Or the opposite? And how would the working out look like?

 

[InteGrand]

Okay, so you used 360, how about if I was to use 180? What would I use? 180/Pi? Or the opposite? And how would the working out look like?

Are you talking about if you wanted to use radians? 180 deg = π rad, so 1 deg = π/180 rad, so

1 minute = 1/60 deg = 1/60 * (π/180) rad = π/10800 rad.

 

[BlueGas]

Are you talking about if you wanted to use radians? 180 deg = π rad, so 1 deg = π/180 rad, so

1 minute = 1/60 deg = 1/60 * (π/180) rad = π/10800 rad.

Yes that's what I wanted. Because I find it easier converting degrees to radians using 180 rather than 360. So how do you get 1/60? Can you explain it if you don't mind please?

 

[BlueGas]

Yes that's what I wanted. Because I find it easier converting degrees to radians using 180 rather than 360. So how do you get 1/60? Can you explain it if you don't mind please?

Nevermind.

 

[InteGrand]

Yes that's what I wanted. Because I find it easier converting degrees to radians using 180 rather than 360. So how do you get 1/60? Can you explain it if you don't mind please?

I didn't "convert to radians" the first time. It's like, if the angle you were given were 90 degrees, you'd have done 1/4*2πR, right? Well, instead of 90 deg, it's 1/60 deg., so instead of 90/360 (= 1/4), it's (1/60)/(360).

 

[InteGrand]

If you're given the angle in degrees, you can just find the arc length using .

 

[InteGrand]

(i.e. )

 

[InteGrand]

So if the arc subtends an angle of 57 degrees say, that's 57/360 of a full circle (since a full circle is 360 degrees), so you'd multiply by to get the length of that arc.

 

[BlueGas]

(i.e. )

Ah, I must have done this question incorrectly then.

The circumference of a circle is 198cm. Calculate the length of arc which subtends an angle of 120 degrees at the centre.

What I did was I found what the radius is by doing 198/2Pi which gives me 31.51 (2.d.p) Then I just did 31.51 x 2Pi/3. Was I wrong? Because I didn't know you can also use the circumference.

By the way, I converted 120 degrees to radians to get 2Pi/3.

 

[BlueGas]

I seem to be confusing myself...

 

[InteGrand]

Ah, I must have done this question incorrectly then.

The circumference of a circle is 198cm. Calculate the length of arc which subtends an angle of 120 degrees at the centre.

What I did was I found what the radius is by doing 198/2Pi which gives me 31.51 (2.d.p) Then I just did 31.51 x 2Pi/3. Was I wrong? Because I didn't know you can also use the circumference.

By the way, I converted 120 degrees to radians to get 2Pi/3.

You don't need the radius at all for this Q. It's very straightforward: .

 

[InteGrand]

I seem to be confusing myself...

Just think about that Q intuitively: if the full circle is 198 cm, then a 120° arc is clearly ⅓ of this. Why? Because getting a 120° arc of the full circle is just ⅓ of the circle!

(Because 120°/360° = ⅓)

 

[BlueGas]

You don't need the radius at all for this Q. It's very straightforward: .

Was my method still correct though?

 

[InteGrand]

Was my method still correct though?

Yes, the method is right, but you'll get some error if you round before the final calculation (and the answer in this case is a whole number).

Plus, when you found the radius, you had to divide by , and then multiply by a again right after, so it's much more efficient in this case just to use straightaway.