Consider the polar axes with the points plotted below.

Question

Picture: https://imgur.com/a/1TNFsvm

A: Write the coordinates of both points A and B in polar form. Be sure to write your radius as a positive value.

B: Plot the point  on the graph and label it as point C.

C: Give two ways to write the coordinates of point C using a positive value for the radius

Answer 1

polar (-3,pi/3) = (3, 4pi/3) = (3, 240 degrees)

reference angle is 60 degrees in quadrant 3

x^2 +(xsqr3)^2 = 3^2 = 9

4x^2 = 9

x^2 = 9/4

x = -3/2 = -1.5

y = (-3/2)sqr3 = -1.5sqr3 = about -2.598

(x,y) = (-1.5, -1.5sqr3) = about (-1.5, -2.598)

Answer 2

Polar coordinates are written with the form: (radius, radian). For question A, and for each point or radius, you identify what radian your line is located at, and then count how many dotted rings your radius covers to find the length of your radius. In simplified terms, polar coordinates are how long your radius is (written first) and what angle your radius is at, measured in radians (written second). Ex: (how long, what angle).

For question B, you find the angle, but instead of marking your radius positively (up), like point B in question A, you measure your radius backward. This radius should end up being in the third quadrant on the graph, but still in line with π/3.

Finally, for question C, you are describing the same point or radius from question B, but in two different ways, with a positive radius. This means that you can't use -3 in your coordinates. To get you started, the first point should have 5π/4 as your radian.

I hope this helps!! Let me know if you need more clarification, and I'd always be happy to schedule a session with you!!