**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

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.

http://thoughtbroadcast.com/tag/mri/

**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

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

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

Cosine = Adj/Hyp

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)