Score : $200$ points

问题陈述

在坐标系为 $xy$ 的平面中，其中 $x$ 轴朝右方向，$y$ 轴向上方向，将一个点 $(a, b)$ 绕原点逆时针旋转 $d$ 度，并求出该点旋转后的新坐标。

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

In an $xy$-coordinate plane whose $x$-axis is oriented to the right and whose $y$-axis is oriented upwards, rotate a point $(a, b)$ around the origin $d$ degrees counterclockwise and find the new coordinates of the point.

Constraints

• $-1000 \leq a,b \leq 1000$
• $1 \leq d \leq 360$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$a$ $b$ $d$

Output

Let the new coordinates of the point be $(a', b')$. Print $a'$ and $b'$ in this order, with a space in between.
Your output will be considered correct when, for each value printed, the absolute or relative error from the answer is at most $10^{-6}$.

Sample Input 1

2 2 180

Sample Output 1

-2 -2

When $(2, 2)$ is rotated around the origin $180$ degrees counterclockwise, it becomes the symmetric point of $(2, 2)$ with respect to the origin, which is $(-2, -2)$.

Sample Input 2

5 0 120

Sample Output 2

-2.49999999999999911182 4.33012701892219364908

When $(5, 0)$ is rotated around the origin $120$ degrees counterclockwise, it becomes $(-\frac {5}{2} , \frac {5\sqrt{3}}{2})$.
This sample output does not precisely match these values, but the errors are small enough to be considered correct.

Sample Input 3

0 0 11

Sample Output 3

0.00000000000000000000 0.00000000000000000000

Since $(a, b)$ is the origin (the center of rotation), a rotation does not change its coordinates.

Sample Input 4

15 5 360

Sample Output 4

15.00000000000000177636 4.99999999999999555911

A $360$-degree rotation does not change the coordinates of a point.

Sample Input 5

-505 191 278

Sample Output 5

118.85878514480690171240 526.66743699786547949770

update @ 2024/3/10 10:59:05