trig question
plotting points given polar coordinates and/or rectangular coordinates
trig question
plotting points given polar coordinates and/or rectangular coordinates
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.
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:)