Counterclockwise Rotation

AtCoder

IDabc259_b

Time2000ms

Memory256MB

Difficulty—

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: $a$ $b$ $d$ [samples]

Samples

Input #1

2 2 180

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 $(-2, -2)$.

Input #2

5 0 120

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.

Input #3

0 0 11

Output #3

0.00000000000000000000 0.00000000000000000000

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

Input #4

15 5 360

Output #4

15.00000000000000177636 4.99999999999999555911

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

Input #5

\-505 191 278

Output #5

118.85878514480690171240 526.66743699786547949770

API Response (JSON)

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  "problem": {
    "name": "Counterclockwise Rotation",
    "description": {
      "content": "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 c",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc259_b"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "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 c...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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