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The Tangent Function Today’s Objective: I can find exact values and graph the tangent function.

x y (1, 0) (0, 1) (-1, 0) (0, -1) 1 SOH CAH TOA = Slope

Domain: Range: Period: x y (1, 0) (0, 1) (-1, 0) (0, -1) All Real #s π

Graphing Tangent Functions a = vertical stretch Sketch the graph of: Graphing: 1.Graph mid-line points origin and end of each period 2.Graph asymptotes: halfway thru period 3.Graph halfway points - Between mid-line and asymptotes Vertical distance a and – a Period:

Graphing: 1.Graph mid-line points origin and end of each period 2.Graph asymptotes: halfway thru period 3.Graph halfway points - Between mid-line and asymptotes Vertical distance a and – a Sketch the graph of: Period: from -2π to 2π Graphing Tangent Functions a = vertical stretch

Translating Trigonometric Functions Today’s Objective: I can write and graph a trigonometric functions.

Think about riding a bike and pumping the pedals at a constant rate of one revolution each second. How does the graph of the height of one of your feet compare with the graph of a sine function?

Translating Functions Horizontal Vertical Phase Shift Translate h units horizontally Translate k units vertically Midline: y = k h

Family of Trigonometric Functions Parent Functions Transformed Function Amplitude: Vertical stretch or shrink Number of cycles in normal period: Phase shift: Horizontal shift Vertical shift : y = k is midline

Graph each function on interval from 0 to 2π Amplitude: Graphing: 1.Sketch in Midline (y = k) 2.Graph beginning point with phase shift. 3.Graph remaining four points. Phase Shift: Midline: Period:

Graph each function on interval from 0 to 2π Amplitude: Graphing: 1.Sketch in Midline (y = k) 2.Graph beginning point with phase shift. 3.Graph remaining four points. Phase Shift: Midline: Period:

Write a sine and cosine function for the graph. Pg. 880 #24-37, 44, 45 Pg. 872 #9-15, 18-25, 30-32, 44-46

Graph each function on interval from 0 to 2π Amplitude: Phase Shift: Midline: Period: