AS Maths - Radians

Hi please explain in simple terms :-)

The diagram shows a circle, centre O, of radius 6 cm. The points A and B are on the circumference of the circle. The area of the shaded major sector is 80cm^2. Given that <AOB = (theta) radians, where 0<theta<pie. calculate:

a) The value, to 3 decimal places, of theta

b) the length in cm, to 2 decimal places, of the minor arc AB

Reply 1

user2020user

16

Original post by KJ_

...

Where's the diagram? :tongue:

Reply 2

Old_Simon

12

In general you need to calculate the Area of the circle, and the length of the whole circumference.

Then you need to calculate what proportion or fraction of those numbers you are being asked for.

Reply 3

interstitial

18

Original post by KJ_

The answer for a should be 1.839 and so far I have got every answer apart from that when I try to work it out

What have you tried?

Posted from TSR Mobile

Reply 4

interstitial

18

Original post by KJ_

80= pi(6)^2(theta) / 2

Do you know how to do the workings?

Rearrange for theta like a normal equation.

Posted from TSR Mobile

Reply 5

TenOfThem

18

Original post by majmuh24

Area=

\dfrac{\pi r^2 \theta}{2}

,
Posted from TSR Mobile

Original post by majmuh24

Multiply by the 2 first, since you have to divide the whole thing by 2, not just the pi part.

Posted from TSR Mobile

Both of these are incorrect

(edited 10 years ago)

Reply 6

TenOfThem

18

Original post by KJ_

Hi please explain in simple terms :-)

The diagram shows a circle, centre O, of radius 6 cm. The points A and B are on the circumference of the circle. The area of the shaded major sector is 80cm^2. Given that <AOB = (theta) radians, where 0<theta<pie. calculate:

a) The value, to 3 decimal places, of theta

b) the length in cm, to 2 decimal places, of the minor arc AB

The area of a sector =

\dfrac{r^2\theta}{2}

Reply 7

TenOfThem

18

Original post by KJ_

Yeah that is what i have in my book but this doesn't give me the right answer either

Yes it does

As long as you realise that it gives you the big angle and theta is the small angle

Reply 8

interstitial

18

Original post by TenOfThem

Both of these are incorrect

Ignore my stupid posts, must have made a mistake with the formula, I'll delete it now :s-smilie:

Reply 9

Old_Simon

12

Original post by KJ_

Yeah that is what i have in my book but this doesn't give me the right answer either

Can someone post some workings please all the equations are confusing me :-(

Bear in mind the question contains a kink. We need to find theta (well you do !!!) but the area we are given is for the major sector. Theta of course is the angle of the minor sector. Just saying.

Reply 10

TenOfThem

18

Original post by KJ_

??

What do you not understand about what I have said

You have a diagram, you know the shaded area is the MAJOR sector

You know that you are looking for the angle in the MINOR sector

This was all in the question