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Intro to Polar Coordinates Review
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Terms in this set (25)
how do we locate a point in a polar coordinate system?
imagining that we started with a vector along the positive x axis and we rotated it through θ until reaching the point
what is θ in polar coordinates?
the angle you rotate through to get to the point
what is r in polar coordinates?
the length of the vector reaching from the origin to the point
on polar coordinate graphs, what do the circles represent?
values of r
what happens when the angle is negative?
you start at the positive x axis and head into quadrant 4
what happens when r is negative?
you go to the angle and then go in the opposite direction (if you were going to go to the r circles in quadrant 2, you would instead go to quadrant 4)
how can you represent polar coordinates in different ways?
you can change the signs on the components and use coterminal angles
when converting to polar coordinates, what is x?
rcosθ
when converting to polar coordinates, what is y?
rsinθ
when converting to polar coordinates, what is tanθ?
y/x
when converting to polar coordinates, what is r²?
x² + y²
What is one way to graph polar equations?
Find values: pick a θ and solve for r
(4, 2π/3)
Determine the polar coordinate from the graph
(4,45°)
Determine the polar coordinate from the graph
(-4,3π/4)
Determine the polar coordinate from the graph
(3,-5π/3)
Determine the polar coordinate from the graph
(-3,-π/2)
Determine the polar coordinate from the graph
(-5,-4π/3)
Determine the polar coordinate from the graph
(2,19π/6)
Determine the polar coordinate from the graph
(-5,13π/4)
Determine the polar coordinate from the graph
(-1,π/6)
Pick the correct alternate form of the polar coordinate (1, 7π/6)
(-3,5π/4)
Pick the correct alternate form of the polar coordinate (3, π/4)
(3,7π/2)
Pick the correct alternate form of the polar coordinate (3, 3π/2)
(-1,11π/6)
Pick the correct alternate form of the polar coordinate (1, 5π/6)
(5,-π/3)
Pick the correct alternate form of the polar coordinate (5, 5π/3)
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