trigonometry · worked example

Solve sin(30°)

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

sin(30°)\sin(30°)

Step-by-step solution

  1. 30°30° 是應該背熟的標準「特殊角」之一。

  2. 以弧度表示:30°=π630° = \frac{\pi}{6}

  3. 在單位圓上,30°30° 處的點座標為 (32,12)\bigl(\frac{\sqrt{3}}{2}, \frac{1}{2}\bigr)

  4. 正弦是 y 座標:sin(30°)=12\sin(30°) = \frac{1}{2}

  5. 幾何驗證:在 30°30°-60°60°-90°90° 三角形中,30°30° 角所對的邊恰好是斜邊的一半 — 直接得出 sin30°=12\sin 30° = \frac{1}{2}

Answer

sin(30°)=12\sin(30°) = \tfrac{1}{2}

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