Right Triangle
Trigonometry
Presenter:
LaShondia McNeal, Ed.D.
Breaking
the Ice
“Solutions to
My Problems”
Each envelope contains either a math
problem or a solution to a problem.
Your Task: Find the person that has the
other.
Ask the following questions:
•What’s your name?
•Where are you from?
•What do you teach?
•How many years of experience in Adult
Education?
Objective:
“Epitome of the Almagest”
As a group of Teachers, Staff,
Administrators and other
Stakeholders seek to recognize,
apply and share learning of triangle
trigonometry and then act on what
is learned for the benefit of the
students.
1.5
What is Triangle Trigonometry?
The study in which angles are
commonly measured in degrees
and trigonometric functions are
defined as ratios of sides of a
right–angled triangle.
Vocabulary
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1.5
The Trigonometric Functions: Sine, Cosine, Tangent,
Cosecant, Secant and Cotangent
Trigonometric Ratios: see slide #12
α: Angle alpha
Terminal side: Hypotenuse
Standard position: Angles with the vertex at the
origin and its initial side lies along positive x-axis.
r: The distance between a point (x,y) on the terminal
side and the origin.
1.5
Right Triangles
Figure 1
Figure 2
Trigonometric Functions of a
Right Triangle
1.5
If α is an acute angle of a right triangle, then
opp
sin  
,
hyp
adj
cos  
, and
hyp
opp
tan  
.
adj
hyp
csc  
,
opp
hyp
sec  
, and
adj
adj
cot  
.
opp
1.5
The Reciprocal Identities
1
csc  
sin 
1
sec  
cos 
1
cot  
tan 
What are possible steps for solving this
problem?
1. Given that  is an angle in standard position whose
terminal side contains the given point, provide the
exact value of the indicated function.
(15,36);sin 
a. 12
13
5
c.  13
b.  12
13
d.
5
13
1.5
What are possible steps for solving this
problem?
2. Find the exact value of the following expression.
No calculator.
1
sec  , if cos  and sin  0
2
a. 2
b.
3
c. 2
d.
3
3
1.5
What is sin(45°) and cos(45°) ?
Figure 4
1.5
What is sin (30°) and cos (30°) ?
Figure 5
1.5
1.5
Web Links and Resources
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www.amatyc.org American Mathematical Association of Two-Year
Colleges
www.ams.org American Mathematical Society
www.analyzemath.com Mathematics tutorials and applications
www.dyscalculia.org/DIC.html Dyscalculia International Consortium
www.hawaii.edu/suremath/home.html 21st Century Problem Solving
www.imacc.org/standards/ Crossroads in Mathematics: Standards for
Teaching College Mathematics Before Calculus
www.maa.org Mathematical Association of America
www.maa.org/cupm Committee on the Undergraduate Curriculum in
Mathematics
www.nctm.org The National Council of Teachers of Mathematics
www.purplemath.com
www.umkc.edu/cad/made National Association for Developmental
Education