Converting Equations from Polar Form to Rectangular Form

First, remind me of the Coordinate Conversion Equations… 2 2 x = r cos

Now, on with the Examples… Convert r = 4 sec 0 to rectangular form

Now, on with the Examples… Convert r = 4 cos 0 to rectangular form

More Examples Convert the given polar equation to rectangular form. Identify the graph, and

Converting Equations from Rectangular Form to Polar Form

Right in with an example… Convert the given rectangular equation to polar form. Identify

Guided Practice Convert the given rectangular equation to polar form. Identify the graph, and

One more use for polar coordinates… Radar tracking often gives location in polar coordinates.

Another Example Using radar, a navy ship locates two enemy ships at polar coordinates

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Converting Equations from Polar Form to Rectangular Form Sec. 6. 4

First, remind me of the Coordinate Conversion Equations… 2 2 x = r cos 0 r = x +y y = r sin 0 y tan 0 = x 2

Now, on with the Examples… Convert r = 4 sec 0 to rectangular form and identify the graph. Support your answer graphically. How did I reach step? ? ? à A vertical line through x = 4! à Check your calculator!

Now, on with the Examples… Convert r = 4 cos 0 to rectangular form and identify the graph. Support your answer graphically. CTS!!! Factor!!! Conversion Equations A circle with center (2, 0) and radius 2

More Examples Convert the given polar equation to rectangular form. Identify the graph, and support your answer graphically. horizontal line

More Examples Convert the given polar equation to rectangular form. Identify the graph, and support your answer graphically. Circle with center (– 2, 0) and radius 2

More Examples Convert the given polar equation to rectangular form. Identify the graph, and support your answer graphically. Circle with center (3/2, 0) and radius 3/2

More Examples Convert the given polar equation to rectangular form. Identify the graph, and support your answer graphically. Circle with center (2, – 2) and radius 2 2

Converting Equations from Rectangular Form to Polar Form

Right in with an example… Convert the given rectangular equation to polar form. Identify the graph, and support your answer graphically. Expanded the binomial!! Conversion Equations Circle with center (1, 0) and radius 1

Guided Practice Convert the given rectangular equation to polar form. Identify the graph, and support your answer graphically. Vertical line

Guided Practice Convert the given rectangular equation to polar form. Identify the graph, and support your answer graphically. Line with slope – 3/4 and y-intercept 1/2

Guided Practice Convert the given rectangular equation to polar form. Identify the graph, and support your answer graphically.

Guided Practice Convert the given rectangular equation to polar form. Identify the graph, and support your answer graphically. OR Check the graph? Circle with center (3, 2) and radius 13

One more use for polar coordinates… Radar tracking often gives location in polar coordinates. Suppose that 2 airplanes are at the same altitude with polar coordinates of (8 mi, 110 ) and (15 mi, 15 ). How far apart are the airplanes? First, let’s see a graph… Next, use the Law of Cosines!!! The airplanes are about 17. 604 miles apart

Another Example Using radar, a navy ship locates two enemy ships at polar coordinates of (5230 m, 130 ) and (6721 m, 155 ). Find the distance between the two enemy ships. The ships are about 2968. 131 meters apart