Post on 02-Jan-2016
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:
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.
“Epitome of the Almagest”
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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.
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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.
Vocabulary
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Figure 1 Figure 2
Right Triangles
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,csc
,sin
opp
hyp
hyp
opp
and adj
hyp
and hyp
adj
,sec
,cos
.cot
.tan
opp
adj
adj
opp
If α is an acute angle of a right triangle, then
Trigonometric Functions of a Right Triangle
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tan
1cot
cos
1sec
sin
1csc
The Reciprocal Identities
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1. Given that is an angle in standard position whose terminal side contains the given point, provide the exact value of the indicated function.
a. b.
c. d.
( 15,36);sin
12
13
12
13
5
13
5
13
What are possible steps for solving this problem?
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2. Find the exact value of the following expression.
No calculator.
a. b.
c. d.
1sec , if cos and sin 0
2
2 3
2 3
3
What are possible steps for solving this problem?
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Figure 4
What is sin(45°) and cos(45°) ?
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Figure 5
What is sin (30°) and cos (30°) ?
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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
Web Links and Resources