Question

vector a is at a 225° angle measured counterclockwise from the positive x - axis. when it is written in components, ( a_x = a ) ( 225^{circ}= ) ( a ), and ( a_y = a ) ( 225^{circ}= ) ( a ). (round to three significant figures.)

Explanation:

Step1: Recall the formula for vector components

The formula for the \(x -\)component of a vector \(\vec{A}\) is \(A_x = A\cos\theta\) and the formula for the \(y -\)component is \(A_y=A\sin\theta\), where \(\theta\) is the angle made with the positive \(x -\)axis.

Step2: Substitute \(\theta = 225^{\circ}\) into the formulas

We know that \(\cos(225^{\circ})=\cos(180^{\circ} + 45^{\circ})=-\cos(45^{\circ})=-\frac{\sqrt{2}}{2}\approx - 0.707\) and \(\sin(225^{\circ})=\sin(180^{\circ}+45^{\circ})=-\sin(45^{\circ})=-\frac{\sqrt{2}}{2}\approx - 0.707\)

Answer:

\(A_x = A\cos(225^{\circ})\approx - 0.707A\), \(A_y = A\sin(225^{\circ})\approx - 0.707A\)