bmarks31
contestada

Which of the following pairs of coordinates represents the same point in polar coordinates? Check all that apply.
(r,theta) and (r,theta+2pi)
(r,theta) and (-r,theta)
(r,theta) and (-r,theta+ 2pi)
(r,theta) and (-r,theta+pi)​

Respuesta :

MrRoyal

A point that has the polar coordinate [tex](r,\theta)[/tex] can also be represented by [tex](r, \theta+2n\pi)[/tex] and [tex](-r, \theta+(2n+1)\pi)[/tex].

From the list of given options, [tex](r,\theta)[/tex] and [tex](-r, \theta+\pi)[/tex] are represents the same point

Recall that:

[tex](r, \theta+2n\pi)[/tex] and [tex](-r, \theta+(2n+1)\pi)[/tex] represents the same point

Where n is an integer

Assume [tex]n = 0[/tex]

[tex](r, \theta+2n\pi)[/tex] becomes

[tex](r, \theta+2n\pi) = (r, \theta+2\times 0 \times \pi)[/tex]

[tex](r, \theta+2n\pi) = (r, \theta+0)[/tex]

[tex](r, \theta+2n\pi) = (r, \theta)[/tex]

Similarly,

[tex](-r, \theta+(2n+1)\pi)[/tex] becomes

[tex](-r, \theta+(2n+1)\pi)=(-r, \theta+(2\times 0+1)\pi)[/tex]

[tex](-r, \theta+(2n+1)\pi)=(-r, \theta+(0+1)\pi)[/tex]

[tex](-r, \theta+(2n+1)\pi)=(-r, \theta+(1)\pi)[/tex]

[tex](-r, \theta+(2n+1)\pi)=(-r, \theta+\pi)[/tex]

This means that: [tex](r,\theta)[/tex] and [tex](-r, \theta+\pi)[/tex] represent the same point.

Hence, (d) is correct.

Read more about polar coordinates at:

https://brainly.com/question/13206882

926kaya

Answer:

There are two correct answers, (r,theta) and (r,theta+2pi) and (r,theta) and (-r,theta+pi)​

Step-by-step explanation:

(r,theta) and (r,theta+2pi) is correct because you can add 2pi as many times as you want and it will still be true, as 2pi is a full circle in radians.

(r,theta) and (-r,theta+pi)​ is true because you can add pi, or 180°, to any polar coordinate and negate the r to make it equivalent, which is exactly what this answer does.

(these are also the right answers on a.pex :) )

good luck!

Otras preguntas