January 30, 2014
Precalc Warm Up #
sin
6-4
Copy and fill out the input output table.
Find sin exact and to nearest 100th.
Graph y = sin
Domain? Range?
Period?
Amplitude?
0
January 30, 2014
January 30, 2014
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(0,1)
135o
(-1,0)
o
120o 90
60o
45o
30o
150o
0
180o
210
0o or 360o
225o
-
330o
o
240o
315o
270o
300o
(0,-1)
(1,0)
January 30, 2014
(0,1)
135o
120o 90o
60o
45o
30o
150o
(-1,0)
0
180o
0o or 360o
330o
210o
225o
240o
315o
270
o
300o
(0,-1)
(1,0)
January 30, 2014
Is sin x odd or even?
ie...is sin(-x) = sin x (even) or is sin (-x) = - sin x (odd?)
b
x
-x
b
a
-a
January 30, 2014
Since sin (-x) = -sin x, y = sin x is odd and therefore has
origin symmetry. What does this mean about the graph?
Graph y = sin x on grapher. Be sure to use an appropriate domain.
On grapher...
Explore y = a sin x
Try many values for a. Make sure to try negatives too.
y = sin x
January 30, 2014
In y = a sin x , the amplitude is _____
Without grapher, sketch 2 periods of y = 4 sin x
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
January 30, 2014
In y = a sin bx, b affects the _____
Without grapher, sketch 2 periods of y = 2 sin 5x
Then graph both y = sinx and y = 2 sin5x on grapher
Now let's explore what c does in y = a sin (bx - c)
f(x) = sin x
g(x) = sin (x - ___ )
2
How does g compare with f ?
f(x) = sin x
g(x) = sin (x - ___ )
2
January 30, 2014
Without Grapher, sketch 2 periods of y = sin (2x +____)
2
dom?
range?
period?
Amplitude?
Graph y = sinx and y = (2x + ____ ) on grapher.
2
In summary,
y = a sin ( bx - c) + d
a affects:
b affects:
c affects:
d affects:
when is there a reflection over x axis?
y axis?
Without your grapher, sketch of y = -4 sin (3x +
dom?
range?
period?
Amplitude?
) +2
January 30, 2014
Sketch without grapher y =sin ( ___ - x)
2
dom?
range?
What does y =sin (
period?
Amplitude?
___
2
- x) equal?
Graph (without using your grapher) y = cos x
(0,1)
135o
o
120o 90
60o
45o
30o
150o
(-1,0)
0
180o
0o or 360o
330o
210o
225
315o
o
240o
270o
300o
(0,-1)
(1,0)
January 30, 2014
Sketch two periods of the graph of y = -3 - cos(
- 2x)
Check with your grapher.
#6-4 p. 352 box. Sketch graphs without graphers.