Polar Coordinates

Notes

Notes for Converting Polar to Cartesian

Notes for Converting Cartesian to Polar

 

\({\text{Equations of Lines}}\)
\(\underline{\text{Polar Form}}\) \(\underline{\text{Cartesian Form}}\)
\(\theta=\beta\)
\(y = (\tan \beta) x \)
\(r \cos \theta=a\)
\(x=a\)
\(r \sin \theta =b\)
\(y=b\)

 

\({\text{Equations of Circles}}\)
\(\underline{\text{Polar Form}}\) \(\underline{\text{Cartesian Form}}\)
\(r=c\)
\(x^2+y^2=c^2\)
\(r= 2a\cos \theta\)
\((x-a)^2+y^2=a^2\)
\(r= 2b\sin \theta\)
\(x^2+(y-b)^2=b^2\)
\(r= 2a\cos \theta + 2b\sin \theta\)
\((x-a)^2+(y-b)^2=a^2+b^2\)

 

\({\text{Equations of Parabolas (Focus on the origin)}}\)
\(\underline{\text{Polar Form}}\) \(\underline{\text{Cartesian Form}}\)
\(r=\frac{p}{1-\sin \theta}\)
\(y=\frac{1}{2p}x^2-\frac{p}{2}\)
\(r=\frac{p}{1+\sin \theta}\)
\(y=-\frac{1}{2p}x^2+\frac{p}{2}\)
\(r=\frac{p}{1-\cos \theta}\)
\(x=\frac{1}{2p}y^2-\frac{p}{2}\)
\(r=\frac{p}{1+\cos \theta}\)
\(x=-\frac{1}{2p}y^2+\frac{p}{2}\)

 

Questions & Videos

\(\textbf{1)}\) Convert the point from Polar to Rectangular Coordinates
\((8,60^{\circ})\) Link to Youtube Video Solving Question Number 1

 

\(\textbf{2)}\) Convert the point from Polar to Rectangular Coordinates
\((2,180^{\circ})\)Link to Youtube Video Solving Question Number 2

 

\(\textbf{3)}\) Convert the point from Rectangular to Polar Coordinates
\((-4,5)\)

 

\(\textbf{4)}\) Convert the point from Rectangular to Polar Coordinates
\((0,-3)\) Link to Youtube Video Solving Question Number 4

 

\(\textbf{5)}\) Convert the Polar Equation to Rectangular and identify the graph
\(r=2 \cos⁡ \theta\) Link to Youtube Video Solving Question Number 5

 

\(\textbf{6)}\) Convert the Polar Equation to Rectangular and identify the graph
\(r=\displaystyle \frac{5}{1-\cos \theta}\)

 

\(\textbf{7)}\) Convert the Polar Equation to Rectangular and identify the graph
\(r=\displaystyle\frac{3}{3+ \sin \theta}\)Link to Youtube Video Solving Question Number 7

 

\(\textbf{8)}\) Convert the Polar Equation to Rectangular and identify the graph
\(r=5\)

 

\(\textbf{9)}\) Convert the Polar Equation to Rectangular and identify the graph
\(r=6 \cos \theta\)

 

\(\textbf{10)}\) Convert the Polar Equation to Rectangular and identify the graph
\(r=-12 \sin \theta\)

 

\(\textbf{11)}\) Convert the Polar Equation to Rectangular and identify the graph
\(r=6 \cos \theta – 8 \sin \theta\)

 

\(\textbf{12)}\) Convert the Polar Equation to Rectangular and identify the graph
\(\theta=\frac{\pi}{4}\)

 

\(\textbf{13)}\) Convert the Polar Equation to Rectangular and identify the graph
\(\theta=-\frac{\pi}{4}\)

 

\(\textbf{14)}\) Convert the Polar Equation to Rectangular and identify the graph
\(r \cos \theta=2\)

 

\(\textbf{15)}\) Convert the Polar Equation to Rectangular and identify the graph
\(r \sin \theta=-3\)

 

\(\textbf{16)}\) Convert the Polar Equation to Rectangular and identify the graph
\(r=\frac{4}{1+ \sin \theta}\)

 

See Related Pages\(\)

\(\bullet\text{ Displacement Vectors}\)
\(\,\,\,\,\,\,\,\,(x_2-x_1)\vec{i}+(y_2-y_1)\vec{j}…\)
\(\bullet\text{ Magnitude, Direction, and Unit Vectors}\)
\(\,\,\,\,\,\,\,\,|\vec{u}|=\sqrt{a^2+b^2}…\)
\(\bullet\text{ Dot Product}\)
\(\,\,\,\,\,\,\,\,a \cdot b=x_1 x_2+ y_1 y_2…\)
\(\bullet\text{ Parallel and Perpendicular Vectors}\)
\(\,\,\,\,\,\,\,\,⟨8,2⟩ \text{ and } ⟨−4,−1⟩…\)
\(\bullet\text{ Scalar and Vector Projections}\)
\(\,\,\,\,\,\,\,\,\displaystyle\frac{a \cdot b}{|b|^2} \, \vec{b}…\)
\(\bullet\text{ Cross Product}\)
\(\,\,\,\,\,\,\,\,\)Thumbnail for Cross Product\(…\)
\(\bullet\text{ Equation of a Plane}\)
\(\,\,\,\,\,\,\,\,Ax+By+Cz=D…\)

 

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