# A Level Further Maths Polar Coordinates

Does anyone know how to do this question? I managed to get the coordinates of the points of intersection but have no clue where to go next.
Here's the question: https://imgur.com/VPHU29Y
And here's the mark scheme (Q5): activeteachonline.com/default/player/document/id/786821/external/0/uid/357726
Original post by Amy.fallowfield
Does anyone know how to do this question? I managed to get the coordinates of the points of intersection but have no clue where to go next.
Here's the question: https://imgur.com/VPHU29Y
And here's the mark scheme (Q5): activeteachonline.com/default/player/document/id/786821/external/0/uid/357726

If you drew a line between the origin and the point of intersection, the first integral represents the area below this line and above asin(2theta). The second integral represents the area above this line and below asin(4theta).
Original post by mqb2766
If you drew a line between the origin and the point of intersection, the first integral represents the area below this line and above asin(2theta). The second integral represents the area above this line and below asin(4theta).

But in the mark scheme, they've used pi/4 for the bounds, where did that come from, since pi/6 is the point of intersection that splits the region?
Original post by Amy.fallowfield
But in the mark scheme, they've used pi/4 for the bounds, where did that come from, since pi/6 is the point of intersection that splits the region?

Youve got to trace the polar cuves out to have some idea about the limits. Both are
r = a sin(k*theta)
so both start heading off along the x axis as you start increasing theta. The relevant section of 2theta is 0..pi/6. The relevant section of 4theta is pi/6.. pi/4. The latter is on the return loop back to the origin, as sin(4*pi/4)=0.
(edited 12 months ago)