trig question

plotting points given polar coordinates and/or rectangular coordinates

trig question

plotting points given polar coordinates and/or rectangular coordinates

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To plot points with polar coordinates we must first understand what the coordinates mean. The first coordinate is the radius and the second is the angle.

To find the point I like to think of it as we start out standing at the pole (origin) and facing the polar axis (positive x-axis). We then rotate through the angle, if it is a positive angle we rotate counter clockwise, a negative angle we rotate clockwise. Once we have rotated appropriately we then walk the radius units along the line we are facing, forward for a positive value and backwards for a negative value. Where we stop is the location of the point.

To find other sets of polar coordinates we have two options. Option 1 is to rotate "extra circles" (or in the opposite direction). We can do this by adding or subtracting multiples of 2pi (or 360 degrees) to the angle. Option 2 is to reverse the direction we are facing and negating the radius. We can do this by adding or subtracting pi (or 180 degrees) to the angle and multiplying the radius by -1.

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## Comments

Hey Lauren!

Visualize a clockface: 9:00 to 3:00 is x-axis; noon down to 6:00 is y.

(2, 40 deg) is clock hand length 2 pointed just before 2:00 --

y= 2 sin (40/60 rads) ==> since sin(rad)= rad for angle< 45 deg --

y= 2* 2/3= 4/3

shortcut for x: r+10% minus 1/2 shorter leg => 2.2 minus 2/3 = 1.53

(x,y) => (1.53, 1.33)

(5, 3pi/2) ==> clockhand of 5 pointed at 6:00, thus (x,y) is (0,-5)... Regards:)