Question

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

Answer 1

V ( Vcos 60° , Vsin60°) or V ( 2, 2√3)

Explanation:

A vector and its components form a right triangle, then we need to get trigonometric functions ( sin and cos) of the angle of the module with x-axis

π/3 = 180⁰/3 = 60⁰ Angle between vector and positive x-axis

and sin 60⁰ = √3 /2 cos 60⁰ = 1/2

Let call V(x) component of vector v in x-axis, and V(y) component of vector v in y-axis then

V(x) = |v|*cos 60⁰ ⇒ V(x) = |v|*1/2 ⇒ V(x) = 4*1/2 ⇒ V(x) = 2

And

V(y) = |v|*sin 60⁰ ⇒ V(y) = |v|*√3/2 ⇒ V(y) = 4*√3/2 V(y) = 2*√3

V = (Vx,Vy) V ( Vcos 60° , Vsin60°) V ( 2, 2√3)