Trigonometry Functions

y = a imes ext{sin}(k(x + q)) + p

The equation describes a sinusoidal function, where 'a' affects amplitude, 'k' affects period, 'q' is horizontal shift, and 'p' is vertical shift.

Amplitude

'a' in the function y = a imes ext{sin}(k(x + q)) + p; it determines the height of the peaks from the midline.

Period for sine and cosine functions

Calculated as $\frac{360}{k}$, where 'k' affects how quickly the wave repeats.

Period for tangent functions

Calculated as $\frac{180}{k}$; tangent functions have a different period from sine and cosine.

Step of a sinusoidal function

Determined by the formula $\frac{\text{period}}{4}$, this represents how much the function increases in one-fourth of its cycle.

Range of a sinusoidal function

Given by [max;min], where max and min are calculated from the amplitude and vertical shift.

Domain of tangent functions

Typically restricted due to vertical asymptotes; it does not include values where the function is undefined.

Horizontal shifts in sinusoidal functions

Given by 'q' in the equation, determining how far left or right the graph moves.

Vertical shift in sinusoidal functions

Given by 'p' in the equation, moving the entire graph up or down.

Max value of a sinusoidal function

Calculated as $p + a$; this is the peak height of the graph.

Min value of a sinusoidal function

Calculated as $p - a$; this is the lowest point of the graph.