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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 C+ B, C+ B, C+ B, C+B. 2 occur when x= C, 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 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.

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 C+ B, C+ B, C+ B, C+B. 2 occur when x= C, 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 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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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 poir (minimums, maximums, and crossing the midline) will +B.C+/B.C+²B.C+B. occur when x= C, C+- 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 900 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: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 poir (minimums, maximums, and crossing the midline) will +B.C+/B.C+²B.C+B. occur when x= C, C+- 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 900 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.
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