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7.4 Polar Coordinates and Graphs Mon March 2 Do Now Evaluate

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Rectangular coordinates All graphing weve done so far has been done with rectangular coordinates (x,y) This is not the only way to describe graphs

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Polar Coordinates A point can be described in polar coordinates The origin is called the pole The positive half of the x-axis is called the polar axis The point can be plotted given an angle from the polar axis and a distance R from the pole to the point

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Graphing Polar Coordinates 1) Locate the directed angle 2) Move a directed distance R from the pole If R > 0, move along the polar axis If R < 0, move in the opposite direction 3) Drawing circles with radius R will help graph each point

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Ex Graph each of the following points A) B) C) D) E) F)

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Convert to Polar Coordinates To convert from rectangular coordinates (x,y) to polar coordinates we create a right triangle that relates rectangular and polar:

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Ex Convert each of the following to polar coordinates 1) 2)

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Converting to Rectangular Coordinates Using the same relationship, we can convert to rectangular coordinates:

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Ex Convert each to rectangular coordinates 1) 2)

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Closure Convert (-4, 4) to polar coordinates HW: p.644 #1-37 odds

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7.4 Polar Equations Day 2 Do Now Graph the polar coordinates 1) 2) 3) 4)

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HW Review: p.644 #1-37

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Polar and Rectangular Equations Some curves have simpler equations in polar coordinates than in rectangular coordinates, and vice versa It can be useful to convert equations so they are easier to work with

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Ex Convert each of the following to a polar equation 1) 2)

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Ex Convert each of the following to a rectangular equation 1) 2) 3)

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You try Convert to polar equations 1) 2) Convert to rectangular equations 3) 4)

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Closure Convert to a rectangular equation HW: p.644 #39-61 odds

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7.4 Graphing Polar Equations Day 3 Do Now Convert to a polar equation

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HW Review p.644 #39-61

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Graphing Polar Equations To graph polar equations, we want to make a table of values Pick angles to plug into the function You should make at least one full revolution of angles to plug in

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Ex Graph

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Ex Graph the polar equation r = 3

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Do Now Graph

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Ex Graph

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Technology For more complicated polar functions, use a graphing calculator The MODE must be set to polar (POL) Once in polar coordinates, the X key can be used to type THETA Note: you may have to change your windows

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1 + 2sinX

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Closure Graph HW: p.644 #63-97 odds (try not to use calculator for 63-69)