Radians
a) The diagram shows a circle with centre O and radius r, and a chord AB which subtends an angle θ radians at O. Express the area of the shaded segment bounded by the chord AB in terms of r and θ.
I managed this fine:
Area of shaded segment = r^2/2 (θ-sinθ)
b) Given that the area of this segment id one-third of the area of the triange OAB, show that 3θ - 4sinθ=0.
No matter how many times and how many different ways i try, i cannot get to that. i always land up with 3θ - 4sinθ = 0.
c) Find the positive value of θ satisfying 3θ - 4sinθ to within 0.1 radians, by tabulating values of 3θ - 4 sinθ and looking for a sign change, or otherwise.
Can't figure this out either....
Thanks for any help!!!!
I managed this fine:
Area of shaded segment = r^2/2 (θ-sinθ)
b) Given that the area of this segment id one-third of the area of the triange OAB, show that 3θ - 4sinθ=0.
No matter how many times and how many different ways i try, i cannot get to that. i always land up with 3θ - 4sinθ = 0.
c) Find the positive value of θ satisfying 3θ - 4sinθ to within 0.1 radians, by tabulating values of 3θ - 4 sinθ and looking for a sign change, or otherwise.
Can't figure this out either....
Thanks for any help!!!!
Original post by Jmun
a) The diagram shows a circle with centre O and radius r, and a chord AB which subtends an angle θ radians at O. Express the area of the shaded segment bounded by the chord AB in terms of r and θ.
I managed this fine:
Area of shaded segment = r^2/2 (θ-sinθ)
b) Given that the area of this segment id one-third of the area of the triange OAB, show that 3θ - 4sinθ=0.
No matter how many times and how many different ways i try, i cannot get to that. i always land up with 3θ - 4sinθ = 0.
c) Find the positive value of θ satisfying 3θ - 4sinθ to within 0.1 radians, by tabulating values of 3θ - 4 sinθ and looking for a sign change, or otherwise.
Can't figure this out either....
Thanks for any help!!!!
I managed this fine:
Area of shaded segment = r^2/2 (θ-sinθ)
b) Given that the area of this segment id one-third of the area of the triange OAB, show that 3θ - 4sinθ=0.
No matter how many times and how many different ways i try, i cannot get to that. i always land up with 3θ - 4sinθ = 0.
c) Find the positive value of θ satisfying 3θ - 4sinθ to within 0.1 radians, by tabulating values of 3θ - 4 sinθ and looking for a sign change, or otherwise.
Can't figure this out either....
Thanks for any help!!!!
For part b), it looks like you've got what they want.
It looks like trial and error for part c).
Original post by Jmun
a) The diagram shows a circle with centre O and radius r, and a chord AB which subtends an angle θ radians at O. Express the area of the shaded segment bounded by the chord AB in terms of r and θ.
I managed this fine:
Area of shaded segment = r^2/2 (θ-sinθ)
b) Given that the area of this segment id one-third of the area of the triange OAB, show that 3θ - 4sinθ=0.
No matter how many times and how many different ways i try, i cannot get to that. i always land up with 3θ - 4sinθ = 0.
c) Find the positive value of θ satisfying 3θ - 4sinθ to within 0.1 radians, by tabulating values of 3θ - 4 sinθ and looking for a sign change, or otherwise.
Can't figure this out either....
Thanks for any help!!!!
I managed this fine:
Area of shaded segment = r^2/2 (θ-sinθ)
b) Given that the area of this segment id one-third of the area of the triange OAB, show that 3θ - 4sinθ=0.
No matter how many times and how many different ways i try, i cannot get to that. i always land up with 3θ - 4sinθ = 0.
c) Find the positive value of θ satisfying 3θ - 4sinθ to within 0.1 radians, by tabulating values of 3θ - 4 sinθ and looking for a sign change, or otherwise.
Can't figure this out either....
Thanks for any help!!!!
So you did part a) by saying the area of the sector is 1/2 r^2 θ and the area of the triangle is 1/2 r^2 sin(θ), and then subtracting those gives you the area of the segment = 1/2 r^2(θ-Sin{θ})
For part b), you're told that this is one third the area of the triangle. In other words:
3 x Segment = Triangle
3x 1/2 r^2(θ-Sin{θ}) = 1/2 r^2 Sinθ
Expand these and collect to the left, you get the answer
And part c) is just trial and error
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