Precalc 4.5 day 40.notebook
December 08, 2016
Warm Ups Day 40
1. f(x) = sin x and g(x) = Take out HW for me to check.
2
x . Evaluate f(g(­3)
2. Sketch f(x) = ­4 + 3(x ­ 2)
without calculator
2
3. Sketch f(x) = |3x + 12| ­ 1
Today we will study techniques for sketching the graphs of of Sine and Cosine functions.
We will explore reflections, horizontal and vertical shifts and stretches, and domain and range.
.
Precalc 4.5 day 40.notebook
December 08, 2016
sin
(0,1)
Graph y = sin
120
o
90
o
(-1,0)
180
0
60o
135o
45o
30o
150o
0
o
0o or 360o
(1,0)
330o
210o
315o
225o
240o
270o
300o
(0,-1)
Domain?
Range?
Period?
Amplitude?
Period?
Amplitude?
.
Graph y = 1 + sin
Domain?
Range?
Precalc 4.5 day 40.notebook
December 08, 2016
On grapher...
Explore y = a sin x
Try many values for a. Make sure to try negatives too.
What is a doing, and why?
y = sin x
In y = a sin x , the amplitude is _____
Vertical stretch, magnitude __
Without grapher, sketch 2 periods of y = 4 sin x
then check on grapher
Precalc 4.5 day 40.notebook
December 08, 2016
In y = a sin x , the amplitude is _____
If a < 0, what happened, and why?
Without grapher, sketch 2 periods of y = ­3 sin x
then check on grapher
Let's explore the effect of b in y = a sin bx
On grapher, graph both y = sin x and y = sin 2x
Try other values for b including negatives. What is happening, and why?
y = sin 2x
y = sin x
Precalc 4.5 day 40.notebook
December 08, 2016
What will the period be for the following? Sketch
y = sin 3x
y = sin x
_x
y = sin 1
3
In y = a sin bx, b affects the _____
horizontal stretch, magnitude:
Without grapher, sketch 2 periods of y = 2 sin 5x
then check on grapher
Precalc 4.5 day 40.notebook
December 08, 2016
In y = a sin bx, b affects the _____
What happened when b was negative?
Without grapher, sketch 2 periods of y = 3 sin (­2x)
y = a sin (bx + c)
a affects amplitude
b affects period
what does c affect?
Precalc 4.5 day 40.notebook
December 08, 2016
Without Grapher, sketch 2 periods of y = sin (x + ____)
2
dom? period?
range? Amplitude?
Without Grapher, sketch 2 periods of y = sin (2x +____)
2
dom?
period?
range? Amplitude?
Precalc 4.5 day 40.notebook
December 08, 2016
Sketch without grapher y =sin ( ___ - x)
2
dom?
period?
range? Amplitude?
What does y =sin (
What does y =sin (
___
2
___
2
- x) equal?
- x) equal?
Precalc 4.5 day 40.notebook
December 08, 2016
Sketch without grapher y =sin ( ___ - x)
2
dom?
period?
range? Amplitude?
Graph again (without using your grapher) y = cos x
(0,1)
o
120o 90
60o
45o
135o
30o
150o
(-1,0)
0
180o
0o or 360o
330
o
210o
225o
315o
240o
300
o
270o
(0,-1)
(1,0)
Precalc 4.5 day 40.notebook
December 08, 2016
Sketch two periods of the graph of y = 2 cos 3x
Check with your grapher.
Sketch two periods of the graph of y = ­3 ­ cos( ­ 2x)
Check with your grapher.
Precalc 4.5 day 40.notebook
December 08, 2016
Summary
y = a cos b(x ­ d) y = a sin b(x ­ d) dom:
range:
amplitude:
period:
reflections:
Which parent graph is odd?
y = sin x
Which parent graph is even?
y = cos x
Precalc 4.5 day 40.notebook
December 08, 2016
What could the equation of the following graphs be?
HW 40 pg 299 1 ­ 8, 11 ­ 41 odd