102591: [AtCoder]ABC259 B - Counterclockwise Rotation

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

题目描述

在一个$x$轴向右、$y$轴向上的坐标平面上，将点$(a, b)$围绕原点逆时针旋转$d$度，找出新点的坐标。

约束条件

• $-1000 \leq a,b \leq 1000$
• $1 \leq d \leq 360$
• 输入中的所有值都是整数。

输入

从标准输入中按照以下格式给出输入：

$a$ $b$ $d$

输出

令新点的坐标为$(a', b')$。按顺序打印$a'$和$b'$，其间用空格隔开。
当每个输出值与答案之间的绝对或相对误差不超过$10^{-6}$时，您的输出将被认为是正确的。

样例输入 1

2 2 180

样例输出 1

-2 -2

当$(2, 2)$围绕原点逆时针旋转$180$度时，它变成了$(2, 2)$关于原点的对称点，即$(-2, -2)$。

样例输入 2

5 0 120

样例输出 2

-2.49999999999999911182 4.33012701892219364908

当$(5, 0)$围绕原点逆时针旋转$120$度时，它变成了$(-\frac {5}{2} , \frac {5\sqrt{3}}{2})$。
这个样例输出与这些值并不完全一致，但是误差足够小，被认为是正确的。

样例输入 3

0 0 11

样例输出 3

0.00000000000000000000 0.00000000000000000000

因为$(a, b)$是原点（旋转中心），旋转不会改变其坐标。

样例输入 4

15 5 360

样例输出 4

15.00000000000000177636 4.99999999999999555911

一个$360$度的旋转不会改变点的坐标。

样例输入 5

-505 191 278

样例输出 5

118.85878514480690171240 526.66743699786547949770