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Tangent Graphs

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Examples, solutions, videos, worksheets, games and activities to help Algebra 2 students learn about the tangent, unit circle and tangent graphs.

How to define the Tangent Function in the Unit Circle?
In right triangle trigonometry (for acute angles only), the tangent is defined as the ratio of the opposite side to the adjacent side.
The unit circle definition is tan(θ)= y/x or tan(θ)=sin(θ)/cos(θ).
The tangent function is negative whenever sine or cosine, but not both, are negative: the second and fourth quadrants. Tangent is also equal to the slope of the terminal side.

How to graph the Tangent Function?
For a tangent function graph, create a table of values and plot them on the coordinate plane.
Since tan(θ) = y/x, whenever x = 0 the tangent function is undefined (dividing by zero is undefined). These points, at θ = π/2, 3π/2 and their integer multiples, are represented on a graph by vertical asymptotes, or values the function cannot equal. Because of unit circle symmetry over the y-axis, the period is π/2.

The tangent ratio as seen in a right triangle and on the unit circle, and why the right triangle definitions of the trig ratios are equivalent to the unit circle definitions.
Graph Tangent and identify key properties of the function
Graph the tangent function on the coordinate plane using the unit circle.
Determine the domain and range of the tangent function.

Animation: Graphing the Tangent Function Using the Unit Circle
Illustrate the graph of the tangent function using the unit circle.
Graphs of trig functions
Exploring the graphs of trig functions

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