Graphs of Sine, Cosine and Tangent Functions | 正弦、余弦和正切函数的图像

📚 Graphs of Sine, Cosine and Tangent Functions | 正弦、余弦和正切函数的图像

The graphs of y = sin x, y = cos x and y = tan x are central to trigonometry. They allow us to solve equations, find ranges and periods, and model oscillations, waves and alternating currents.

y = sin x、y = cos x 和 y = tan x 的图像是三角学的核心内容。借助图像，我们可以解三角方程、确定值域和周期，并用来模拟振动、波动和交变电流等周期现象。

1. From the Unit Circle to the Graph | 从单位圆到图像

On the unit circle, an angle θ measured in radians determines a point (cos θ, sin θ). The sine value is the vertical coordinate of that point.

在单位圆上，以弧度为单位的角度 θ 对应一个点 (cos θ, sin θ)，其中正弦值就是该点的纵坐标。

As θ increases from 0 to 2π, the y-coordinate first rises from 0 to 1, returns to 0, falls to -1, and finally returns to 0.

当 θ 从 0 增大到 2π 时，纵坐标先从 0 上升到 1，再回到 0，然后下降到 -1，最后又回到 0。

Plotting θ horizontally and sin θ vertically gives a smooth, repeating wave called a sine curve.

以 θ 为横坐标、sin θ 为纵坐标作图，就得到一条光滑且不断重复的波浪形曲线，称为正弦曲线。

2. The Graph of y = sin x | 正弦函数 y = sin x 的图像

The sine graph passes through the origin and has a maximum value of 1 and a minimum value of -1.

正弦曲线经过原点，最大值为 1，最小值为 -1。

Its period is 2π, so the pattern repeats every 2π radians.

它的周期是 2π，即每隔 2π 弧度图案重复一次。

The following exact values are useful when sketching the curve.

画图时以下特殊值非常有用。

At every multiple

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