Question

Find the polar equation that has the same graph as the equation in x and y: x = -3

Answer 1

\[x=r \cos \theta=-3=3*-1,r=3,\cos \theta=-1=\cos \pi,\theta=\pi \]
polar co-ordinates are (3,pi )

Answer 2

x = -3 => x+3 = 0
which will give the ordered pair of (-3, 0)

whilst x = -3, y = 0
\(\bf r = \sqrt{(-3)^2+0^2} \implies r = 3\\
tan\left(\frac{0}{-3}\right) = 0 \implies tan^{-1}(0) = \pi\)

Answer 3

According to the back of my book (because it is an odd problem), the answer is \[r = -3 \sec \theta\]

Answer 4

I just don't know how to get that..

Answer 5

in all honesty, I can see r = -3 and +3
while the angle being 0 or pi and both values will yield a -3

Answer 6

\[r=3 \cos \pi \]

Answer 7

r is always positive

Answer 8

@jdoe0001 okay, so what about the sec (theta)

Answer 9

\(\bf x = rcos(\theta) \textit{ thus then}\\
x = -3 \implies rcos(\theta) = -3 \implies r = \cfrac{-3}{cos(\theta)}\\
r = \cfrac{-3}{1} \cdot \cfrac{1}{cos(\theta)}\)

Answer 10

Great!! Thank you!! @jdoe0001