Question

5. (a) Draw a suitable a polar grid and plot the curve whose equation in polar coordinates is ( r=6 sin ( heta) ) for ( 0 leq heta leq pi ). Use intervals of length ( frac{pi}{6} ). In your table of values, display the values of ( heta ) in both radians and degrees. [9 marks] (b) Use a double integral in polar coordinates to determine the area of the region which lies inside the curve ( r=6 sin ( heta) ) (from part (a)) but outside the circle centred at the origin and of radius ( 3 sqrt{2} ). You may assume that these two curves meet at the points ( (-3,3) ) and ( (3,3) ). Note: The following identity may be useful. [ sin ^{2}(A)=frac{1-cos (2 A)}{2} . ] [16 marks]

          5. (a) Draw a suitable a polar grid and plot the curve whose equation in polar coordinates is ( r=6 sin (	heta) ) for ( 0 leq 	heta leq pi ). Use intervals of length ( frac{pi}{6} ).
In your table of values, display the values of ( 	heta ) in both radians and degrees.
[9 marks]
(b) Use a double integral in polar coordinates to determine the area of the region which lies inside the curve ( r=6 sin (	heta) ) (from part (a)) but outside the circle centred at the origin and of radius ( 3 sqrt{2} ).
You may assume that these two curves meet at the points ( (-3,3) ) and ( (3,3) ). Note: The following identity may be useful.
[
sin ^{2}(A)=frac{1-cos (2 A)}{2} .
]
[16 marks]

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$5. (a) Draw a suitable a polar grid and plot the curve whose equation in polar coordinates is ( r=6 sin ( heta) ) for ( 0 leq heta leq pi ). Use intervals of length ( fracpi6 ). In your table of values, display the values of ( heta ) in both radians and degrees. [9 marks] (b) Use a double integral in polar coordinates to determine the area of the region which lies inside the curve ( r=6 sin ( heta) ) (from part (a)) but outside the circle centred at the origin and of radius ( 3 sqrt2 ). You may assume that these two curves meet at the points ( (-3,3) ) and ( (3,3) ). Note: The following identity may be useful. [ sin ^2(A)=frac1-cos (2 A)2 . ] [16 marks]$

Added by Anna D.

Calculus of a Single Variable

Ron Larson 11th Edition

Chapter 10

Instant Answer

Solved by Expert Zack A

08/09/2023

Step 1

| \( \theta \) (radians) | \( \theta \) (degrees) | \( r \) | |------------------------|------------------------|---------| | 0 | 0 | 0 | | \( \frac{\pi}{6} \) | 30 | 3 | | \( Show more…

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Polar grids and polar Coordinates

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