A series of free online Trigonometry Video Lessons.
Examples, solutions, videos, worksheets, and activities to help Trigonometry students.
In this lesson, we will learn
Sine and cosine are periodic functions, which means that sine and cosine graphs repeat themselves in patterns. You can graph sine and cosine functions by understanding their period and amplitude. Sine and cosine graphs are related to the graph of the tangent function, though the graphs look very different.
How to graph the sine and cosine function on the coordinate plane using the unit circle?
How to determine the domain and range of the sine and cosine function?
How to determine the period of the sine and cosine function?
The coefficients A and B in y = Asin(Bx) or y = Acos(Bx) each have a different effect on the graph. If A and B are 1, both graphs have an amplitude of 1 and a period of 2pi. For sine and cosine transformations, when A is larger than 1, the amplitude increases and is equal to the value of A; if A is negative, the graph reflects over the x-axis. When B is greater than 1, the period decreases; use the formula 2pi/B to find the period.
Amplitude and Period of Sine and Cosine
This video explains how to determine the amplitude and period of sine and cosine functions. It also shows how to graph the sine and cosine functions with different amplitudes and periods.
In the equation y = Asin(B(x-h)) or y = Acos(B(x-h)) , A modifies the amplitude and B modifies the period; see sine and cosine transformations. The constant h does not change the amplitude or period (the shape) of the graph. It shifts the graph left (if h is negative) or right (if h is positive) and in the amount equal to h. The amount of horizontal shift is called the phase shift, which equals h.
Graph Sine and Cosine functions with the four basic transformations: amplitude, period, phase shift and vertical shift.