plot each point whose polar coordinates are given. Then give two other pairs of polar coordinates for the point. (2, 40deg; (5,, 3pi/2)

Question

trig question

plotting points given polar coordinates and/or rectangular coordinates

Answer 1

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.