February 8 th copyright2009merrydavidson Warm up: Factor These. 1)y 2 – 812) cos 2 x – 9 3)z 2 - 7z + 104) sin 2 x – 5sinx – 6 5) x 2 + 2x – 86) tan 2 x + tanx - 12

All Students Take Classes Tells you where the trig functions are positive and/or negative. A S T C The period for tangent/ cotangent is or pi radians The tangent graph repeats every 180 0

Tangent is undefined at _____________. Tangent is zero at __________________. Tangent is positive in quadrants _______. +(90 0,270 0 ) 0 0 +(180 0,360 0 ) I & III Asymptotes start ½ period on EITHER SIDE of the y-axis. (go 1 period each way for the next asymptote)

Fill in the remaining parts of the Tangent Parent Function page.

Graphing Tangent Start with a point on the origin (or with phase shift at “start”). Draw in asymptotes ½ period to the right and left of the “start”. Draw in more asymptotes 1 period to the right and left. Draw in “up on the right, down on the left”.

-270 o -180 o o 90 o 180 o 270 o Asymptotes at x= +(90,270) 0 Asymptotes start on either side of where you started!

EX 1:y = tan shifts _________ so start at ______ 0 none B = ______ Find the period: 3; P = 60 0 Go ½ period to the right and left of start and draw in/label asymptotes. Go 1 period to the right and left for another set of asymptotes Sketch in the curves and place in the y axis. 0 y-axis x-axis

EX 2:y = tan shifts _________ so start at ______ Right 10 0 B = ______ Find the period: ½; P = Go ½ period to the right and left of start and draw in/label asymptotes. Go 1 period to the right and left for another set of asymptotes Sketch in the curves and place in the y axis. 10 y-axis x-axis

EX 3: y = -2tan ( )x y-axis x-axis

HW: worksheet 8-1