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## 13.6 – The Tangent Function

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**I. Graphing the Tangent Function**• The tangent of an angle is derived from the coordinates of a point on a line that is tangent to a circle. • Tangent θ – the y – coordinate of the point where the line containing the terminal side of the angle intersects the tangent line x = 1.**THINK: TANGENT = OPPOSITE/ADJACENT**• Therefore, the tangent is equal to sin/cos**Sketch the graph of the tangent function, using a table from**0 2π**Notice as you graph the tangent function it, approaches**infinity, and thus has asymptotes at specified values.**II. Properties of y = a tan b θ**• There is no amplitude • Once cycle occurs in the interval from (-π/2b) to (π/b) π/b is the period of the function there is vertical asymptotes at each end of the cycle**Example 1: graph the following:**• A) y = 50 tan θ • B) f(x) = tan (π/6)θ**Example 2: solve the following:**• A) tan θ = 2 • B) 6 tan θ = 1