calculate the x and y components of the vector given below. do not round any intermediate computations, and…

Explanation:

Step1: Recall vector - component formula

For a vector of magnitude $r$ and angle $\theta$ with the positive x - axis, the x - component $x = r\cos\theta$ and the y - component $y=-r\sin\theta$ (negative because the vector is in the fourth - quadrant). Here, $r = 23$ and $\theta = 33^{\circ}$.

Step2: Calculate the x - component

$x=r\cos\theta=23\cos(33^{\circ})$. Using a calculator, $\cos(33^{\circ})\approx0.8387$, so $x = 23\times0.8387=19.2901\approx19.29$.

Step3: Calculate the y - component

$y=-r\sin\theta=- 23\sin(33^{\circ})$. Using a calculator, $\sin(33^{\circ})\approx0.5446$, so $y=-23\times0.5446=-12.5258\approx - 12.53$.

Answer:

$x = 19.29$ $y=-12.53$