三角學

正弦與餘弦的三角變換

了解振幅、週期、相位平移和垂直平移如何改變正弦與餘弦圖形，以進行準確的三角建模。

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媒體報導

Forbes

Problem

Create a video about trigonometric transformations with sound.

Step 1: Identify the Transformation Parameters

To transform a trigonometric function like

y = a\sin(b(x-h)) + k,

first identify the parameters.

The value $a$ changes the amplitude, $b$ adjusts the period, $h$ shifts the graph horizontally, and $k$ moves it vertically.

By applying these values sequentially, you can graph any periodic function accurately.

概念

Graphs of Trigonometric Functions

The graphs of $y = \sin x$ , $y = \cos x$ , and $y = \tan x$ , and how amplitude, period, phase shift, and midline change with the general form $y = A\sin(Bx - C) + D$ .

Sinusoidal Modeling

Using sine or cosine functions to model periodic real-world phenomena such as temperature cycles, tides, and circular motion. Determine the amplitude, period, phase shift, and midline from the data.

Function Transformations

A unified framework for transforming any function's graph: horizontal and vertical shifts, reflections over the axes, and horizontal and vertical stretches/compressions. The order of transformations matters.

更多影片

驗證 cot x · sin x = cos x

驗證 cot x · sin x = cos x

正弦和餘弦圖形變換

利用週期性化簡 sin(theta - 360°)

利用週期性化簡 sin(theta - 360°)

以直角分量求合向量

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