FP2 polar coordinates help please
Hi, doing a paper and there's two questions I'm stuck on and can't find the answers anywhere,
any help muchly appreciated!
1. The curve C is given by: π θ
r=2(cosθ)^(3/2), -π/2 , θ , π/2
a) Find the area enclosed by C. (7)
At the point A on C, θ=a where 0<a<π/2,and the tangent at A to C is parallel to the initial line.
c) Find, to 2 d.p, the value of a and the corresponding value of r. (7)
2. The diagram above shows a sketch of the curve C with polar equation:
r=4sinθ(cosθ)^2 0<_θ<_ π/2
The tangent to C at the poin P is perpendicular to the initial line.
a) show that P has polar coordinates (3/2,π/6) (6)
The point Q on C has polar coordinates (√2,π/4)
The shaded region R is bounded by OP,OQ and C, as shown in the diagram above.
b)show that the area of R is given by
π/2
∫ π/6(cos2θ(sin2θ)^2 + 1/2 - 1/2 cos4θ) dθ (3)
c) Hence, or otherwise, find the area of R, giving your answer in the for a+bπ, where a and b are rational numbers (5)
Thanks!
any help muchly appreciated!
1. The curve C is given by: π θ
r=2(cosθ)^(3/2), -π/2 , θ , π/2
a) Find the area enclosed by C. (7)
At the point A on C, θ=a where 0<a<π/2,and the tangent at A to C is parallel to the initial line.
c) Find, to 2 d.p, the value of a and the corresponding value of r. (7)
2. The diagram above shows a sketch of the curve C with polar equation:
r=4sinθ(cosθ)^2 0<_θ<_ π/2
The tangent to C at the poin P is perpendicular to the initial line.
a) show that P has polar coordinates (3/2,π/6) (6)
The point Q on C has polar coordinates (√2,π/4)
The shaded region R is bounded by OP,OQ and C, as shown in the diagram above.
b)show that the area of R is given by
π/2
∫ π/6(cos2θ(sin2θ)^2 + 1/2 - 1/2 cos4θ) dθ (3)
c) Hence, or otherwise, find the area of R, giving your answer in the for a+bπ, where a and b are rational numbers (5)
Thanks!
Original post by james22
What have to tried so far?
for 1. a) i got (8a^2)/3 by integrating r^2 between the limits
for 1. b) i put it in form of "y=" using y=rsin(theta) and then differentiating it dy/d(theta) and putting it equal to zero, but haven't got the answer yet.
no idea for q2.
EDIT:
got answer now for b) which is (theta) = pi/6 , r=0.81
(edited 9 years ago)
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