1. 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:

2. 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

3. 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

4. Recall how y = x2 is related to y = x2 + 1
Recall how y = x2 is related to y = x 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

5.  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

6. 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

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

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

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

10.  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

11. 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 = ___________

12. 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 = _____________

13. 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 = _____________

14. 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 = _____________

15. Finish the worksheet!