Trigonometry
三角學
Trigonometry studies the sides and angles of triangles. In this lesson you will learn about right-angled triangles and how to use sine, cosine and tangent.
三角學研究三角形的邊和角。在這一課，你會學習直角三角形，以及怎樣使用正弦、餘弦和正切。
1 · Right-angled triangles
直角三角形
A right-angled triangle has one 90-degree angle. The longest side, opposite the right angle, is the hypotenuse. The side across from an angle is the opposite, and the side next to it is the adjacent.
直角三角形有一個 90 度的角。最長的邊（對著直角的邊）是斜邊。對著角的邊是對邊，貼著角的邊是鄰邊。
2 · SOH CAH TOA
SOH CAH TOA
We use three ratios to solve right triangles: sine, cosine and tangent. Remember them with SOH CAH TOA:
我們用三個比率來解直角三角形：正弦、餘弦和正切。用 SOH CAH TOA 來記：
- Sine = Opposite / Hypotenuse正弦 = 對邊 / 斜邊。
- Cosine = Adjacent / Hypotenuse餘弦 = 鄰邊 / 斜邊。
- Tangent = Opposite / Adjacent正切 = 對邊 / 鄰邊。
3 · Finding a side
找邊
To find a side, choose the right ratio. If you know an angle and the hypotenuse, use sine to find the opposite: opposite = hypotenuse × sin(angle).
要找一條邊，先選對的比率。如果知道角和斜邊，用正弦找對邊：對邊 = 斜邊 × sin(角)。
4 · Finding an angle
找角
To find an angle, use the inverse functions. If you know the opposite and the hypotenuse, then angle = inverse sine of (opposite ÷ hypotenuse).
要找角，用反函數。如果知道對邊和斜邊，那麼角 = 反正弦（對邊 ÷ 斜邊）。
5 · Quick check
小測驗