Detailed Analysis of Sine Function Parameters

The fourth page provides in-depth analysis of how parameters affect the sine function.

Definition: The period formula is given by b·p = 2π, where b is the parameter from the function equation.

Example: For f(x) = -3sin(x+1) + 0.5:

• Amplitude is 3
• Period is 2π
• Vertical shift is 0.5

Highlight: The parameter b doesn't directly indicate the stretch factor in the x-direction; this must be calculated separately.

Understanding the Unit Circle and Basic Trigonometric Functions

The first page introduces fundamental concepts of trigonometric functions using the unit circle. The coordinates (u,v) of any point P on the unit circle correspond to cosine and sine values respectively.

Definition: The unit circle is a circle with radius 1 centered at the origin, where coordinates (u,v) represent (cos(α), sin(α)) for any angle α.

Example: For angle 60°, the coordinates are: u = cos(60°) = 0.5 v = sin(60°) = 0.866

Highlight: Trigonometric values repeat every 360°, leading to the relationship: sin(x + n·360°) = sin(x) and cos(x + n·360°) = cos(x)

Vocabulary: The term "Einheitskreis" refers to the unit circle, which is fundamental for understanding trigonometric functions.