If v lies in the first quadrant and makes an angle 𝜋/3 with the positive x-axis and |v| = 4, find v in component form.

Answer 1

The x and y coordinates in terms of r and θ are as follows: (x, y) = (r•cosθ, r•sinθ). So just plug in your values of r=4 and θ=^π/₃.

x = 4•cos^π/₃ = 2

y = 4•sin^π/₃ = 2√3

So the component form of this vector is〈2, 2√3〉.