To plot: Thepoints which has polar coordinate (2,7π4) also two alternaitve sets for the same.

Let the point (2,7π4) be denoted by P. Consider the point (2,7π4), it is 2 units from the Origin O and line OP makes an angle of 7π4 with the positive direction of the x-axis. Add pi to the angle and change cardinal coordinate to -2 to get one alternate solution. Therefore, the point P (2,7π4) can also be represented by (−2,7π4+π)=(−2,11π4). Change the radial coordinate to -2 and subtract 3π from the angle to obtain the other alternate solution. Thus, the point P(2,7π4) can be given by (−2,7π4−3π) =(−2,−19π4). Use online graphing calculator and plot the points of P as shown below in Figure 1. From the Figure 1 it can be noted that alternate representations are plotted on the same location.

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College
Algebra
Linear algebra
Alternate coordinate systems

Suman Cole

Answered question

2021-03-02

To plot: Thepoints which has polar coordinate

(2, \frac{7 π}{4})

also two alternaitve sets for the same.

Answer & Explanation

Dora

Skilled2021-03-03Added 98 answers

Let the point $(2, \frac{7 π}{4})$ be denoted by P.
Consider the point $(2, \frac{7 π}{4})$ , it is 2 units from the Origin O and line OP makes an angle of $\frac{7 π}{4}$ with the positive direction of the x-axis.
Add pi to the angle and change cardinal coordinate to -2 to get one alternate solution.
Therefore, the point P $(2, \frac{7 π}{4})$ can also be represented by $(- 2, \frac{7 π}{4} + π) = (- 2, \frac{11 π}{4}) .$
Change the radial coordinate to -2 and subtract $3 π$ from the angle to obtain the other alternate solution.
Thus, the point $P (2, \frac{7 π}{4})$ can be given by $(- 2, \frac{7 π}{4} - 3 π)$
$= (- 2, - \frac{19 π}{4}) .$
Use online graphing calculator and plot the points of P as shown below in Figure 1.

From the Figure 1 it can be noted that alternate representations are plotted on the same location.

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