1. Which is NOT part of an accurate description the region given by the polar bo
ID: 2832776 • Letter: 1
Question
1. Which is NOT part of an accurate description the region given by the polar bounds 2 r S 5,3m/4 5m/4. (A) It is a wedge shaped region in between circles of radius 2 and 5 (B) It starts at an angle of 7 above the negative x-axis and sweeps clockwise T/4 to an angle of 4 below the negative x-axis. (C) The edge of the inner circle is not included (D) The edge of the outer circle is included 2. When converted to rectangular coordinates, the points (a) (2,2T/3), (b) (4,3T), (c) (-2, -5T/6) have rectangular coordinates (a) (A, B), (b) (C, D), (c) (E, F) respectively. Four of the numbers A, B, C, D, E, F are integers (the other two are both V3). Enter the sum of those four integers. 3. When converted to Cartesian form, the curve r 2 sin 6 2 cos 0 has the form (z -A)2 (y B)2 2. Enter the sum A B 4. When converted to polar form, the curve 2 y 9 has the form r A. What is A?Explanation / Answer
1) figure int his question area between circle of radius 2 and radius 5 but for angle given
so B) option is not correct
2) coordinates are
A = 2 cos 2pi/3 = -1
B = 2 sin 2pi/3 = sqrt3
C = 4 cos 3pi = -4
D= 4 sin 3pi = 0
E = -2 cos(-5pi/6) = sqrt 3
F = -2 sin (-5pi/6) = 1
sum of those fours integers = -1-4+0+1 = -4
c) r = 2sin z + 2 cos z
as we know r = x^2 + y^2
and r cosz = x and r sinz = y
r^2 = 2rsinz + 2rcosz
x^2 + y^2 = 2 x + 2y
x^2 -2x + y^2 - 2y = 0
(x-1)^2 + (y-1)^2 = 2
So A= 1 and B=1
A + B =2
d) let x= r cosz
y = r sinz
so putting in equation
we get r^2 cos^2(z) + r^2sin^2(z) = 9
r^2 [cos^2(z) + sin^2(z)] = 9
r^2 = 9
r=3
so A= 3
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