The rectangular coordinate of [tex]\mathbf{(4,\pi)}[/tex] is (-4,0)
The polar coordinate is given as:
[tex]\mathbf{(4,\pi)}[/tex]
To represent the polar coordinates properly, we make use of:
[tex]\mathbf{(r,\theta) = (4,\pi)}[/tex]
Where r represents radius
The rectangular coordinate is represented as: (x,y)
Where:
[tex]\mathbf{x = rcos(\theta)}[/tex]
[tex]\mathbf{y = rsin(\theta)}[/tex]
So, we have:
[tex]\mathbf{x = 4 \times cos(\pi)}[/tex]
Evaluate cos(pi)
[tex]\mathbf{x = 4 \times -1}[/tex]
Multiply
[tex]\mathbf{x = -4}[/tex]
Similarly,
[tex]\mathbf{y = 4 \times sin(\pi)}[/tex]
Evaluate sin(pi)
[tex]\mathbf{y = 4 \times 0}[/tex]
Multiply
[tex]\mathbf{y = 0}[/tex]
Recall that the rectangular coordinate is represented as (x,y)
Hence, the rectangular coordinate of [tex]\mathbf{(4,\pi)}[/tex] is (-4,0)
Read more about coordinates at:
https://brainly.com/question/13078615
