trigonometry · worked example

Solve cos(60°)

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

cos(60°)\cos(60°)

Step-by-step solution

  1. 60°60° 是值得記住的標準「特殊角」之一。

  2. 以弧度表示:60°=π360° = \frac{\pi}{3}

  3. 在單位圓上,60°60° 處的點座標為 (12,32)\bigl(\frac{1}{2}, \frac{\sqrt{3}}{2}\bigr)

  4. 餘弦就是 x 座標:cos(60°)=12\cos(60°) = \frac{1}{2}

  5. 幾何驗證:在 30°30°-60°60°-90°90° 三角形中,與 60°60° 角相鄰的邊是斜邊的一半 — 證實 cos60°=12\cos 60° = \tfrac{1}{2}

Answer

cos(60°)=12\cos(60°) = \tfrac{1}{2}

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