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# To fill: The blanck spaces in the statement " The origin in the rectangular coordinate system concedes with the ? in polar coordinates. The positive x-axis in rectangular coordinates coincides with the ? in polar coordinates". # To fill: The blanck spaces in the statement " The origin in the rectangular coordinate system concedes with the ? in polar coordinates. The positive x-axis in rectangular coordinates coincides with the ? in polar coordinates".

Question
Alternate coordinate systems asked 2021-02-09
To fill: The blanck spaces in the statement " The origin in the rectangular coordinate system concedes with the ? in polar coordinates. The positive x-axis in rectangular coordinates coincides with the ? in polar coordinates".

## Answers (1) 2021-02-10
The two different ways of locating a point in a plane are the rectangular coordinates and polar coordinates. In polar coordinate system, each point on a plane is determined by a distance from a reference point and an angle from the reference direction. It is represented by $$\displaystyle{\left({r},\theta\right)}$$, where r denotes the distance from the reference point and $$\displaystyle\theta$$ denotes the angle that it makes with the reference direction.
But in the rectangular coordinate system, each point in a plane is determined by a pair of coordinates and represented in the form of (x, y).
So, in rectangular coordinate system the origin coincides with origin in polar and axis in the rectangular coordinate system is the polar axis in the polar coordinate system because an extended line from the reference point is the axis and it denotes the direction of point from the pole in both the coordinate systems.
So, both representations are similar but their nature will vary.
The pole and the polar coordinate arerepresented as the figure given below. ### Relevant Questions asked 2021-02-08

To find: The equivalent polar equation for the given rectangular-coordinate equation.
Given:
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To find: The equivalent polar equation for the given rectangular-coordinate equation.
Given:
$$\displaystyle\ {x}=\ {r}{\cos{\theta}}$$
$$\displaystyle\ {y}=\ {r}{\sin{\theta}}$$
b. From rectangular to polar:
$$\displaystyle{r}=\pm\sqrt{{{x}^{{{2}}}\ +\ {y}^{{{2}}}}}$$
$$\displaystyle{\cos{\theta}}={\frac{{{x}}}{{{r}}}},{\sin{\theta}}={\frac{{{y}}}{{{r}}}},{\tan{\theta}}={\frac{{{x}}}{{{y}}}}$$
Calculation:
Given: equation in rectangular-coordinate is $$\displaystyle{y}={x}$$.
Converting into equivalent polar equation -
$$\displaystyle{y}={x}$$
Put $$\displaystyle{x}={r}{\cos{\theta}},\ {y}={r}{\sin{\theta}},$$
$$\displaystyle\Rightarrow\ {r}{\sin{\theta}}={r}{\cos{\theta}}$$
$$\displaystyle\Rightarrow\ {\frac{{{\sin{\theta}}}}{{{\cos{\theta}}}}}={1}$$
$$\displaystyle\Rightarrow\ {\tan{\theta}}={1}$$
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To determine:
a) Whether the statement, " The point with Cartesian coordinates $$\displaystyle{\left[\begin{array}{cc} -{2}&\ {2}\end{array}\right]}$$ has polar coordinates $$\displaystyle{\left[{b}{f}{\left({2}\sqrt{{{2}}},\ {\frac{{{3}\pi}}{{{4}}}}\right)}\ {\left({2}\sqrt{{{2}}},{\frac{{{11}\pi}}{{{4}}}}\right)}\ {\left({2}\sqrt{{{2}}},\ -{\frac{{{5}\pi}}{{{4}}}}\right)}\ {\quad\text{and}\quad}\ {\left(-{2}\sqrt{{2}},\ -{\frac{{\pi}}{{{4}}}}\right)}\right]}$$ " is true or false.
b) Whether the statement, " the graphs of $$\displaystyle{\left[{r}{\cos{\theta}}={4}\ {\quad\text{and}\quad}\ {r}{\sin{\theta}}=\ -{2}\right]}$$ intersect exactly once " is true or false.
c) Whether the statement, " the graphs of $$\displaystyle{\left[{r}={4}\ {\quad\text{and}\quad}\ \theta={\frac{{\pi}}{{{4}}}}\right]}$$ intersect exactly once ", is true or false.
d) Whether the statement, " the point $$\displaystyle{\left[\begin{array}{cc} {3}&{\frac{{\pi}}{{{2}}}}\end{array}\right]}{l}{i}{e}{s}{o}{n}{t}{h}{e}{g}{r}{a}{p}{h}{o}{f}{\left[{r}={3}{\cos{\ }}{2}\ \theta\right]}$$ " is true or false.
e) Whether the statement, " the graphs of $$\displaystyle{\left[{r}={2}{\sec{\theta}}\ {\quad\text{and}\quad}\ {r}={3}{\csc{\theta}}\right]}$$ are lines " is true or false. asked 2020-12-29
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