Gif v lies in the first quadrant and makes an angle π/3 with the positive x-axis and |v| = 8, find v in component form.

First, illustrate the problem into a diagram like the one shown in the attached picture. The component vectors are shown in red (y-component) and blue (x-component). Since this is a right triangle, let's apply the trigonometric functions of sine and cos.

y-component, vy:
sin (π/3) = vy/8
vy = 6.928

x-component, vx:
cos (π/3) = vx/8
vx = 4