Question

Please help! The polar coordinates (8, 7π/4) represent the Cartesian point
a. (4, 4)
b. (4√2, 4√2)
c. (-4√2, 4√2)
d. (4√2, -4√2)

Answer 1

\[
x= \rho \cos(\theta)\\
y= \rho \sin(\theta)
\]

Answer 2

Use
\[
\rho= 8\\
\theta= 7\pi/4
\]

Answer 3

Notice that
\[7\pi/4 = 2 \pi - \pi/4
\]

Answer 4

Are you there?

Answer 5

i've got x= 8cos(7pi/4) and y=8sin(7pi/4)

Answer 6

How much is the cos and the sin of your angle and you will be done.

Answer 7

\[
\cos(\pi/4) = \sin(\pi/4)= \frac { \sqrt 2}2
\]

Answer 8

It is easy to find your result now.

Answer 9

\[
\cos( 2 \pi -\theta) = \cos(-\theta) =\cos(\theta)
\]

Answer 10

\[
\sin( 2 \pi -\theta) = \sin(-\theta) =-\sin(\theta)
\]

Answer 11

Can you finish it now?