Any questions from your homework Be prepared to

Any questions from your homework? Be prepared to start notes right away.

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

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

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

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 Tangent Functions a = vertical stretch Sketch the graph of: from -2π to 2π 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:

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

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: Midline: Period: Phase Shift: Graphing: 1. Sketch in Midline (y = k) 2. Graph beginning point with phase shift. 3. Graph remaining four points.

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