pencil, highlighter, calculator, red pen, assignment U8P2D3 pencil, highlighter, calculator, red pen, assignment Have out: Bellwork Find each angle value exactly. a) b) y Hints: Show a unit circle. Graph the angle. Draw a reference triangle (if possible). Find the value of the trig ratio at that angle. x total:

a) b) y y θ 1 θ α x x α 1 recall: = 45° = 30° total: +2 +2 +1 graphed angle θ 1 +2 labeled triangle +1 angle θ α x x α +2 triangle 1 +1 recall: = 45° = 30° total: +1

Graphing y = a sin(bx) + k and y = a cos(bx) + k vertical shift Practice # 1: Sketch one positive period of y = –sin 3x. 1 |a| = ___ y 2 3 b = ___ 1 x p = ___ –1

Recall how y = x2 is related to y = x2 + 1 Recall how y = x2 is related to y = x2 + 1. For any function f(x), y = f(x) + k is a _______ shift. If k is _________, shift ___, or if k is ________, shift _____. Sketch y2 = –sin 3x + 1 on the previous axes. vertical positive up negative down y y2 = –sin 3x + 1 2 1 y = –sin 3x x –1

 Steps for graphing y = a sin bx + k : 1. Identify ___, ___, and ___. a b p 2. Make a light sketch of ___________ (without the vertical shift) y = a sin (bx) Identify the major points of interest on the sketch (__________________________________) all intercepts, maximums, and minimums Shift the all the points of interest ____ units up or ____ units down. Graph y = a sin bx + k. k k

Practice # 2: Sketch one positive period of each function Practice # 2: Sketch one positive period of each function. Use radian measure. a)  Shift down 3 units y 2 |a| = ___ 2 x b = ___ –2 –4 p = ___ –6 –8 –10

b) y 2 |a| = ___ 1 b = ___ . x p = ___ –1

c) y 2 |a| = ___ 2 3 b = ___ x . –2 p = ___ –4 –6

y d) 3 |a| = ___ 4 3 2 b = ___ 1 . x p = ___ –1 –2 –3 –4

 Steps for writing the equation y = a sin bx + k: line equilibrium Identify the ____ of ___________. Take the average of the max and min. Identify ____, ____, and ____. Determine ____ by counting the number of units the graph is shifted up or down from the _________. a b p k x – axis

Practice # 3: Determine a y = a sin bx + k or y = a cos bx + k for each function. 1 period 1 period x 3 2 3 sin (2x) + 2 |a| = ____ b = ____ p = ____ y = ___________

Practice # 3: Determine a y = a sin bx + k or y = a cos bx + k for each function. 2 cos – 2 2 |a| = ____ b = ____ p = ____ y = _____________

Practice # 3: Determine a y = a sin bx + k or y = a cos bx + k for each function. 5 –5 sin + 3 |a| = ____ b = ____ p = ____ y = _____________

Practice # 3: Determine a y = a sin bx + k or y = a cos bx + k for each function. 1 period –3 cos – 2 3 |a| = ____ b = ____ p = ____ y = _____________

Finish the worksheet!