Rotating the point p = (3, 3√3) counterclockwise about the origin

[GloriousGoats]

My problem reads as follows: Point p=(3,3√3) is rotated counterclockwise about the origin by 75 degrees. What are the coordinates after this rotation?
I have no idea how to rotate a point, let alone by 75 degrees. Also, I do not know how to start this problem.

 

[Dr.Peterson]

My problem reads as follows: Point p=(3,3√3) is rotated counterclockwise about the origin by 75 degrees. What are the coordinates after this rotation?
I have no idea how to rotate a point, let alone by 75 degrees. Also, I do not know how to start this problem.

There are several ways you could do this, depending on what you have learned (special angles? angle addition formulas? rotation matrices? ...). Please give us some background information, so we can see where to start in trying to help you.

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[pka]

My problem reads as follows: Point p=(3,3√3) is rotated counterclockwise about the origin by 75 degrees. What are the coordinates after this rotation?
I have no idea how to rotate a point, let alone by 75 degrees. Also, I do not know how to start this problem.

We will assume that you have shown no work because you have no idea where to start?
Do you know how far the point $\displaystyle P: (3, 3\sqrt3)$ is from the origin? If not talk with your teacher.
If we rotate $\displaystyle P$ about the origin any number of degrees then will it be the same distance from the origin?
If we label the new rotated point $\displaystyle P'$ and the origin $\displaystyle \mathcal{O}$ will $\displaystyle m( < P \mathcal{O}P')=75^o?$
Now do you have any more ideas of where you might start?