Polar coordinates
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Given the polar coordinates, find the cartesian coordinates of
i) \(A(2,\dfrac{\pi}{4})\)
ii) \(B(3,\pi )\)
$$\begin{align}
&\begin{aligned}\text { (i) }\quad
x &=r \cos 8 \\
y &=r \sin \theta \\
x &=2 \cos \frac{\pi}{4} \\
&=2 \times \frac{\sqrt{2}}{2} \\
&=\sqrt{2} \\
y &=2 \sin \frac{\pi}{+} \\
&=2 \times \frac{\sqrt{2}}{2} \\
&=\sqrt{2} \\
\therefore A &(\sqrt{2}, \sqrt{2})
\end{aligned}\\
&\begin{aligned}\text{(ii)}\quad x &=3 \cos \pi \\ &=-3 \\ y &=3 \sin \pi \\ &=0 \\ \therefore &=3(-3,0) \end{aligned}
\end{align}
$$
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