2D Vectors: Conversions

To convert from magnitude and angle to components, use trigonometry:

$x$-component: $x = r \cdot \cos(\theta)$

$y$-component: $y = r \cdot \sin(\theta)$

For a vector with magnitude $r = 5$ at angle $\theta = 37°$ counterclockwise from the $x$-axis:

• $x = 5 \cdot \cos(37°) = 5 \cdot 0.8 = 4$
• $y = 5 \cdot \sin(37°) = 5 \cdot 0.6 = 3$

The vector has components $(4, 3)$.