Question

Determine the direction angle (in degrees) for each vector:• Make sure you're using degrees instead of radians.• If you use a decimal approximation, you must be accurate to at least 3 decimal places.a. (5, 3) has direction angle: 0 =b. (-4,5) has direction angle: 0 =c. (8,-8) has direction angle: 0=d. (-12, -3) has direction angle: 0=

Answer 1

Step-by-step explanation

a vectors makes a rigth angle to the x-positve axis , so

so, the x coordinate is adjacent side and the y-coordinate becomes into the opposite side, then we can use a trigonometric function that relates those values,it is

`\begin{gathered} tan\theta=\frac{opposi\text{te side}}{adjacent\text{ side}} \\ tan\theta=\frac{y\text{ coordinate}}{x\text{ coordinate}} \end{gathered}`

hence

Step 1

a)

let

`\begin{gathered} \langle5,3\rangle, \\ x=5 \\ y=3 \end{gathered}`

replace and solve for the angle

`\begin{gathered} tan\theta=\frac{y\text{coord\imaginaryI nate}}{x\text{coord\imaginaryI nate}} \\ tan\theta=(3)/(5) \\ \theta=\tan^(-1)((3)/(5)) \\ \theta=30.964° \end{gathered}`

so,

a)Blank1: 30.964

Step 2

b)

let

`\begin{gathered} \langle-4,5\rangle, \\ x=-4 \\ y=5 \end{gathered}`

replace and solve for the angle

`\begin{gathered} tan\theta=\frac{y\text{coord\imaginaryI nate}}{x\text{coord\imaginaryI nate}} \\ tan\theta=(5)/(-4) \\ \theta=\tan^(-1)((5)/(-4)) \\ \theta=-51.340\~+180(Iquadrant) \\ \theta=128.660 \\ . \end{gathered}`

so,

b)Blank2:128.660

Step 3

c)

`\begin{gathered} \langle8,-8\rangle, \\ x=8 \\ y=-8 \end{gathered}`

replace and solve for the angle

`\begin{gathered} tan\theta=\frac{y\text{coord\imaginaryI nate}}{x\text{coord\imaginaryI nate}} \\ tan\theta=(-8)/(8) \\ \theta=\tan^(-1)(-1) \\ \theta=-45 \end{gathered}`

so,

c)Blank3:-45 °

Step 4

d)

`\begin{gathered} \langle-12,-3\rangle, \\ x=-12 \\ y=-3 \end{gathered}`

replace and solve for the angle

`\begin{gathered} tan\theta=\frac{y\text{coord\imaginaryI nate}}{x\text{coord\imaginaryI nate}} \\ tan\theta=(-3)/(-12) \\ \theta=\tan^(-1)((1)/(4)) \\ \theta=14.036 \end{gathered}`

so,

direction

`\begin{gathered} direcgtion\text{ =}\theta+180=14.036 \\ angle=194.036 \end{gathered}`

graph

d)Blank4: 194.036

I hope this helps you