Converting Equations from Polar Form to Rectangular Form

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Presentation transcript:

Converting Equations from Polar Form to Rectangular Form Sec. 6.4

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

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 each step??? A vertical line through x = 4! 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 horizontal line Convert the given polar equation to rectangular form. Identify the graph, and support your answer graphically. horizontal line

More Examples Circle with center (–2, 0) and radius 2 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 Circle with center (3/2, 0) and radius 3/2 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 Circle with center (2, –2) and radius 2 2 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!! Circle with center (1, 0) and radius 1 Conversion Equations

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

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. 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.

Circle with center (3, 2) and radius 13 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

The ships are about 2968.131 meters apart Another Example Using radar, a navy ship locates two enemy ships at polar coordinates of (5230m, 130 ) and (6721m, 155 ). Find the distance between the two enemy ships. The ships are about 2968.131 meters apart