Polar form of a vector
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Write each of the following vectors in component form
i) \([4,45^\circ]\)
ii) \([2,-120^\circ]\)
\begin{align}
&\begin{aligned}\text{i)}\quad x=& r\cos\theta \\
x&=4 \cos 45^{\circ} \\
& =4 \times \frac{\sqrt{2}}{2} \\
&=2 \sqrt{2}\\
y&=r \sin \theta\\
y &=4 \sin 45^{\circ} \\
&=4 \times \frac{2}{\sqrt{2}} \\
&=2 \sqrt{2}
\\ V=\, & 2 \sqrt{2} i+2 \sqrt{2}j
\end{aligned}\\
&\begin{aligned}\text{ii)}\quad \quad x &=2 \cos \left(-120^{\circ}\right) \\
x &=2 \cos \left(120^{\circ}\right) \\
x &=-2 \cos 60^{\circ} \\
&=-2\times\frac{1}{2} \\
&=-1\\
y&=2 \sin \left(-120^{\circ}\right) \\
y &=-2 \sin \left(120^{\circ}\right) \\
y &=-2 \sin 60^{\circ} \\
&=-2 \times \frac{\sqrt{3}}{2} \\
&=-\sqrt{3} \\
V&=-i-\sqrt{3}j
\end{aligned}
\end{align}
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