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trigonometry · worked example

Solve tan(45°) = 1

Method: 特殊角. Verified step-by-step solution with our free AI math solver.
Problem

tan⁡(45°)\tan(45°)

Step-by-step solution

  1. 45°45° 對應到 45-45-90 等腰直角三角形。

  2. 兩股長相等，所以對邊/鄰邊 = 11。

  3. 因此 tan⁡(45°)=1\tan(45°) = 1。

  4. 同樣地，在單位圓上 45°45° 處：sin⁡=cos⁡=22\sin = \cos = \frac{\sqrt{2}}{2}，所以 tan⁡=sin⁡/cos⁡=1\tan = \sin/\cos = 1。

Answer

tan⁡(45°)=1\tan(45°) = 1

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