Question

Convert (5, (3pi)/4) to rectangular coordinates.

Answer 1

\[\left(\color{red}{5}~,~\color{blue}{\frac{3\pi}{4}}\right) \implies (\color{red}{r},\color{blue}{\theta)}\]\[x=\color{red}{r}\cos(\color{blue}{\theta})\]\[y=\color{red}{r}\sin(\color{blue}{\theta})\]

Answer 2

You can figure it out now :)

Answer 3

5cos(3pi/4)=-5/√2

5sin(3pi/4)=5/√2

Answer 4

the answer looks like b.

Answer 5

You're right.

Answer 6

http://www.wolframalpha.com/input/?i=5cos%283pi%2F4%29

http://www.wolframalpha.com/input/?i=5sin%283pi%2F4%29

Answer 7

You can simply tell by looking at the unit circle, at \(\frac{3\pi}{4}\), x is negative and y is positive. and \(\frac{3\pi}{4} \implies \frac{ \sqrt{2}}{2}\)