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# Trigonometry in Medicine

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## Ceara Wettemann

on 13 February 2014

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#### Transcript of Trigonometry in Medicine

Trigonometry in Medicine
Ceara Wettemann
What is Trigonometry?
Trigonometry is the study of angles and the angular relationships of planar and 3D figures.
Six Functions:
Sine
Cosine
Tangent
Cosecant
Secant
Cotangent
Applications in Medicine:
MRIs
Orthopedics
Heart Rate
Breathing
Blood Pressure
Medical
Imaging

Medical Imaging is the process of producing an image of a part of the body using radiographic techniques.
MRI
Magnetic Resonance Imaging
Huge magnet
Lines up all the hydrogen atoms in the body in the direction of the magnet.
Computer gets the data from the spinning protons as mathematical data
Converts to picture
http://themommaven.com/2012/07/my-mri-experience/
How does it relate to trigonometry?
Triangulation is used to determine a specific location in the image that is created.

Orthopedics
Branch of
medicine dealing
with bones.
http://spacemath.gsfc.nasa.gov/transits/TRACEvenus.html
How does it relate to trigonometry?
Determining plate size needed for an open fracture.
If angle is 20 degrees
What is the length of the plate needed?
Length of bone = 4 inches
Plate needed = x
The length can be found using the trig function Cosine.
Cos(20) = x/4
x= 1.63 inches

For example, finding the location
of a tumor in the brain.
Sinusoidal
Graphs

A sinusoidal graph is a graph with successive waves or curves. There are cosine graphs and sine graphs.
http://home.windstream.net/okrebs/page73.html
http://www.mathsisfun.com/algebra/trig-sin-cos-tan-graphs.html
Sinusoidal Graphs in Medicine
Heart rate
Breathing rate/lung capacity
Blood Pressure

Fetal Sinusoidal Heart Rate
Indicate serious fetal issues
Severe Anemia
Hypoxia
Asphyxia
Typically fatal
Important for doctors to recognize the sine wave so that immediate action can be taken.
Amplitude:
5 to 15 bpm
Period:
2 to 5 cycles per minute
http://www.perifacts.eu/cases/Case_681_Sinusoidal_Fetal_Heart_Rate_Patterns.php
Breathing

Spirometer is used to measure volume of air during breathing.
http://www.woodleyequipment.com/clinical-trials/spirometry/spirometer-86-80-505.php
Spirometer produces spirogram, which can be quantified using trigonometry.
http://www.tiem.utk.edu/~gross/bioed/webmodules/lungcapacity.html
Baseline
Angle
Angle
http://drbraindrop.wordpress.com/
SOHCAHTOA
Blood Pressure
When heart contracts, blood pressure rises, when heart relaxes, it drops.
This can be graphed as a sinusoidal wave.
The amplitude
is the maximum blood flow.
http://math.arizona.edu/~maw1999/blood/trig.html
The period is the heart rate.
http://webdocs.cs.ualberta.ca/~database/MEMS/sma_mems/bone.html
http://www.houstonspineandjoint.com/bone-fracture-types.htm
http://www.fetalmonitorstrips.com/learn_more.html
SOURCES
"Case #681 - SINUSOIDAL FETAL HEART RATE PATTERNS." PeriFACTS.eu. Ed. James R. Woods, Jr. N.p.,
n.d. Web. 6 Feb. 2014. <http://www.perifacts.eu/cases/Case_681_Sinusoidal_Fetal_Heart_Rate_Patterns.php>.

Gould, RT-(R)(MR)(ARRT), Todd A., and Molly Edmonds. "How MRI Works" 25 October 2010.
HowStuffWorks.com. <http://science.howstuffworks.com/mri.htm> 05 February 2014.

Sweha, Amir, Trevor Hacker, and Jim Nuovo. "Interpretation of the Electronic Fetal Heart Rate During
Labor." American Family Physician. American Academy of Family Physicians, 1 May 1999. Web. 6 Feb. 2014. <http://www.aafp.org/afp/1999/0501/p2487.html>.

Tisnes, Alejandra. "Medicine and Trigonometry." Math and Trigonometry. N.p., n.d. Web. 4 Feb. 2014. <http://mathandtrigonometry.blogspot.com/>.

"Triangulation." Wikipedia. Wikimedia Foundation, 20 Jan. 2014. Web. 6 Feb. 2014.
<http://en.wikipedia.org/wiki/Triangulation>.

Turner, Josh. "Modern Uses of Trigonometry." EHow. Demand Media, 05 Apr. 2011. Web. 4 Feb. 2014.
<http://www.ehow.com/info_8166929_modern-uses-trigonometry.html>.

Weisstein, Eric W. "Trigonometry." From MathWorld--A Wolfram Web
Resource. http://mathworld.wolfram.com/Trigonometry.html

http://www.fetalmonitorstrips.com/learn_more.html
s(Sin A)(Sin B)
D=
(Sin A + B)
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