Trigonometric Graphs
Graphing sine, cosine, and tangent functions with transformations
lessons (10)
Graphing the Sine Function
Learn to graph the sine function and understand its key properties like amplitude, period, and phase.
Graphing Cotangent
Learn to graph the cotangent function and understand its key features including asymptotes, period, and transformations.
Graphing the Cosine Function
Learn how to graph the cosine function, understand its key features, and explore transformations.
Amplitude and Period
Learn how amplitude and period transform sine and cosine waves and control their height and width.
Graphing Secant and Cosecant
Learn to graph the secant and cosecant functions by understanding their relationship to cosine and sine.
Graphing the Tangent Function
Learn to graph y = tan(x), identify asymptotes, period, and key features of the tangent curve.
Phase Shift
Learn how a phase shift moves sine and cosine graphs left or right, why a minus sign means right, and how to find the shift in sin(Bx - c).
Vertical Shift
Learn how the constant D in y = A sin(x) + D moves a sine or cosine wave up or down, sets its midline and decides its maximum, minimum and range.
Transformations of Trig Graphs
Graph any sine or cosine function of the form y = A sin(B(x - C)) + D: what each parameter does, the right order of transformations and the five key points method.
Writing Trig Equations from Graphs
Read the maximum, minimum, period and a starting point from a wave and turn them into y = A sin(B(x - C)) + D or a cosine equation.
Graphing trigonometric functions reveals their periodic nature. Understanding amplitude, period, phase shift, and vertical shift allows you to graph sine, cosine, tangent, and their reciprocals, as well as model real-world periodic phenomena.
What Students Will Learn
- Graph basic sine and cosine functions
- Identify amplitude, period, and shifts
- Graph tangent and cotangent functions
- Apply transformations to trig graphs
- Model periodic phenomena
Frequently Asked Questions
What is amplitude?
Amplitude is the distance from the midline to a maximum (or minimum). For y = A·sin(x), amplitude is |A|. It measures the height of the wave.
How do I find the period?
For y = sin(Bx) or cos(Bx), period = 2π/|B|. The period is how long before the function repeats. Standard sine and cosine have period 2π.
What causes phase shift?
Phase shift comes from a horizontal translation inside the function. For y = sin(x - C), the phase shift is C units to the right.