Chapter 6.1, Problem 4QR

Solution

To find: The value of $x$ and $y$ .

  $\begin{array}{l}x=3.856\\ y=-4.596\end{array}$

Given information:

Find the value of $x$ and $y$ .

  

Concept used:

The angle is formed by the clockwise rotation. So, the angle is negative.

Use the trigonometric function of angle to find the value of $x$ and $y$ .

Explanation:

The distance of $\left(x,y\right)$ from the origin is $6$ .

Since the angle is formed by the clockwise rotation, the angle is $-50°$ .

The perpendicular side in reference triangle is $y$ , the adjacent side is $x$ and the hypotenuse is $6$ .

Find $y$ .

  $\begin{array}{l}\sin \left(-50°\right)=\frac{\text{perpendicular}\text{side}}{\text{hypotenuse}}\\ \Rightarrow -0.7660=\frac{y}{6}\left[\sin \left(-50°\right)\approx -0.7660\right]\\ \Rightarrow y=-0.7660\times 6\\ \Rightarrow y=-4.596\end{array}$

Find $x$ .

  $\begin{array}{l}\cos \left(-50°\right)=\frac{\text{adjacent}\text{side}}{\text{hypotenuse}}\\ \Rightarrow 0.6428=\frac{x}{6}\left[\cos \left(-50°\right)\approx 0.6428\right]\\ \Rightarrow x=0.6428\times 6=3.8568\end{array}$