Steps to Sketching the Sinusoidal Functions: 1. Lightly sketch the midline line y = D. The midline "splits" the graph into upper and lower halves. 2. Lightly sketch the horizontal lines y=D+A and y=D-A. These two lines determine a horizontal strip inside which the graph of the sinusoidal function will oscillate. Notice, the points where the sinusoidal function has a maximum value lie on the line y = D+ |A|. Likewise, the points where the sinusoidal function has a minimum value lie on the line y = D-|A|. 3. Lightly sketch the vertical lines at x = C and x=C+B. One cycle of the sinusoidal function will lie between these two lines. 4. Sketch one cycle of the sinusoidal function in the box created by steps 2 & 3. The important points (minimums, maximums, and crossing the midline) will 3 occur when x = C, C+÷B,C- C++ B,C + B,C + B, C+B. a. Sine, A > 0: mid-max - mid - min - mid Sine, A < 0: mid - min - mid - max - mid b. Cosine A > 0: max - mid- min - mid - max Cosine A < 0: min - mid-max - mid - min bbana 5. The fact that the function is periodic tells us to simply repeat the graph in th intervals C + B≤ x ≤ C+ 2B, C-B≤ x ≤ C, etc.
Steps to Sketching the Sinusoidal Functions: 1. Lightly sketch the midline line y = D. The midline "splits" the graph into upper and lower halves. 2. Lightly sketch the horizontal lines y=D+A and y=D-A. These two lines determine a horizontal strip inside which the graph of the sinusoidal function will oscillate. Notice, the points where the sinusoidal function has a maximum value lie on the line y = D+ |A|. Likewise, the points where the sinusoidal function has a minimum value lie on the line y = D-|A|. 3. Lightly sketch the vertical lines at x = C and x=C+B. One cycle of the sinusoidal function will lie between these two lines. 4. Sketch one cycle of the sinusoidal function in the box created by steps 2 & 3. The important points (minimums, maximums, and crossing the midline) will 3 occur when x = C, C+÷B,C- C++ B,C + B,C + B, C+B. a. Sine, A > 0: mid-max - mid - min - mid Sine, A < 0: mid - min - mid - max - mid b. Cosine A > 0: max - mid- min - mid - max Cosine A < 0: min - mid-max - mid - min bbana 5. The fact that the function is periodic tells us to simply repeat the graph in th intervals C + B≤ x ≤ C+ 2B, C-B≤ x ≤ C, etc.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
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Transcribed Image Text:Steps to Sketching the Sinusoidal Functions:
1. Lightly sketch the midline line y = D.
The midline "splits" the graph into upper and lower halves.
2. Lightly sketch the horizontal lines y=D+A and y = D-A.
These two lines determine a horizontal strip inside which the graph of the
sinusoidal function will oscillate. Notice, the points where the sinusoidal
function has a maximum value lie on the line y = D + |A|. Likewise, the
points where the sinusoidal function has a minimum value lie on the line y =
D-|A|.
3. Lightly sketch the vertical lines at x = C and x=C+B.
One cycle of the sinusoidal function will lie between these two lines.
4. Sketch one cycle of the sinusoidal function in the box created by steps 2 & 3.
The important points (minimums, maximums, and crossing the midline) will
B, C+B.
occur when x= C, C+-B,
x= C, C+ B, C+ B, C+ B₁C
4
2
4
a. Sine, A > 0: mid-max - mid - min - mid
Sine, A < 0: mid - min - mid - max - mid
b. Cosine A > 0: max - mid - min - mid - max
Cosine A < 0: min - mid-max - mid - min
5. The fact that the function is periodic tells us to simply repeat the graph in the
intervals C + B ≤ x ≤ C + 2B, C - B ≤ x ≤ C, etc.
Transcribed Image Text:b)
a)
Exercise: Sketch one cycle of the following sinusoidal curves. Clearly mark the
scale on the grids.
2π
a) y=-3 cos
x+
3 3
If the coefficient of x is negative,
rewrite the equation using
cos(-) = cos(8)
Identify A, B, C, and D
A =
C =
B =
D=
+1
b) y=2sin -2x+
-2
If the coefficient of x is negative,
rewrite the equation using
sin (-0)=-sin (0)
Identify A, B, C, and D
A =
C =
B =
D =
Expert Solution
Step 1: To find.
In this question, we will find the sinosoidal curve.
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