For the rectangular coordinates 08 a plot the point and b gi

For the rectangular coordinates (0,-8). (a) plot the point, and (b) give two pairs of polar coordinates for the point, where 0° s0360 (a) Choose the correct graph of (0, -8) below. O C. O D. 12 12 12 17 12 17 12 (b) Give two pairs of polar coordinates for the point (0,-8), whereO\'s

Solution

1) a) Graph for (0, -8) is option A)

b) given: point (x = 0, y = -8) with 0° < 360°
polar coordinate equations:
x = r cos()
y = r sin()
or
0 = r cos()
-8 = r sin()
0 = r cos() ========> = 90, 270
hence to find the radius r
-8 = r*sin90 ===> r = -8

and -8 = r*sin270 ===> r = 8
hence one point is:
(r = -8, = 90°)
another point is:
(r = 8 , = 270°)

3) a) Option A)

r = 11*sec = 11/cos

Put cos = x/r

Then r = 11*(r/x)

=====> x = 11 ========> equivalent equation in rectangular coordinates.

b) Option D) is correct graph for x = 11

4) a) x^2 + y^2 = 16

In polar form, x = r*cos    and    y = r*sin

Then given equation becomes,   r^2 = 16

                                                     r = 4 ======> equation in polar form

b) Option A) is correct graph for r = 4