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

V (Vcos 60°, Vsin60°) or V (2, 2√3)

Step-by-step 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)