📚 Graphs of Sine, Cosine and Tangent Functions | 正弦、余弦与正切函数图像
Trigonometric functions are among the most important periodic functions in mathematics. Their graphs display a repeating wave-like pattern that arises from the rotation of a point around the unit circle. In this revision article, we will examine the graphs of y = sin x, y = cos x and y = tan x, together with their transformations, reciprocal functions and applications in solving equations.
三角函数是数学中最重要的周期函数之一。它们的图像呈现出由单位圆上的点旋转而产生的重复波动模式。在本复习文章中，我们将研究 y = sin x、y = cos x 与 y = tan x 的图像，以及它们的变换、倒数函数和在解方程中的应用。
1. The Sine Curve | 正弦曲线
The graph of y = sin x is a smooth, continuous wave that oscillates between 1 and -1. Its basic shape is often described as a series of alternating “humps”.
y = sin x 的图像是一条平滑、连续的波浪曲线，在 1 与 -1 之间振荡。它的基本形状常被描述为一系列交替的”驼峰”。
The sine curve passes through the origin, and its key turning points and intercepts repeat every 2π radians (360°).
正弦曲线经过原点，其关键极值点和零点每 2π 弧度（360°）重复一次。
Key features of y = sin x:
y = sin x 的关键特征：
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Domain: all real numbers; Range: -1 ≤ sin x ≤ 1.
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定义域：全体实数；值域：-1 ≤ sin x ≤ 1。
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Period: 2π (360°); Amplitude: 1.
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周期：2π（360°）；振幅：1。
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Zeroes at x = nπ, where n is an integer.
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零点位于 x = nπ，其中 n 为整数。
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Maximum value 1 at x = π/2 + 2nπ; minimum value -1 at x = 3π/2 + 2nπ.
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最大值 1 出现在 x =
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