Rotate Point p: How to Rotate by 75° Counterclockwise

[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.

 

[Olinguito]

Hint 1: The matrix
$$\begin{pmatrix}\cos\theta & -\sin\theta \\ \sin\theta & \cos\theta\end{pmatrix}$$
represents a counterclockwise rotation of $\theta$ about the origin.

Hint 2: $75^\circ\ =\ 45^\circ+30^\circ$.

 

[MarkFL]

The way I would approach this is:

1.) Find the distance \(r\) from the origin to the given point, and find the angle of inclination \(\theta=\arctan(m)\), where \(m\) is the slope of the line through the origin and the given point. Let \(\alpha=\theta+75^{\circ}\).

2.) The rotated point will then be:

\(\displaystyle (r\cos(\alpha),r\sin(\alpha))\)

 

[LCKurtz]

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.

If you think about where the point p is and where it will be after the rotation, you won't need any rotation formulas or addition formulas, just the basic angles. Draw a picture.