Trigonometry allows finding the result for the decomposition of the displacement vector is:
x = 2.12 mi
y = -2.12 mi
Displacement is a vector quantity, which has modulus and direction.
The cardinal points are a reference system with respect to which measurements are made, this system is related to the Cartesian system with the East in the positive direction of the x-axis and the North with the positive direction of the y-axis.
In the attached we can see a diagram of the vector and its components, the indicated direction of 45 S of the E, in the Cartesian system where the angles are measured from the positive side of the x-axis in a counterclockwise direction is:
θ = 360 - 45
θ = 315º
Let's use trigonometry to decompose the vector d = 3 mi
cos 315 =
sin 315 =
x = d cos 315
y = d sin 315
Let's calculate
x = 3 cos 315
y = 3 sin 315
x = 2.12 mi
y = -2.12 mi
The negative sign indicates that the displacement is towards the negative side, that is, towards the South.
In conclusion using trigonometry we can find the result for the decomposition of the displacement vector are:
x = 2.12 mi
y = -2.12 mi
Learn more here: brainly.com/question/1666179
