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”

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.

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.

Vocabulary

1.5

Figure 1 Figure 2

Right Triangles

1.5

,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

1.5

tan

1cot

cos

1sec

sin

1csc

The Reciprocal Identities

1.5

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?

1.5

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?

1.5

Figure 4

What is sin(45°) and cos(45°) ?

1.5

Figure 5

What is sin (30°) and cos (30°) ?

1.5

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