Download Unit 1

GSE Pre-Calculus
20152016
Unit One Information
Curriculum Map: Unit Circle – Trigonometric Functions (Adv.Alg– Unit 5)
Content Descriptors:
Concept 1: Right Triangle Trig Review
Concept 2: Unit Circle – Radians/Arc Length/Trig Ratios
Concept 3: Co-terminal and Reference Angles
Content from Frameworks: Trigonometric Functions
Unit Length: Approximately 10 days
TCSS – GSE Pre-Calculus – Unit 1
Curriculum Map
Big Idea / Unit
Understand all aspects of the unit circle.
Unit Essential Questions:
How does the unit circle apply to trig
functions?
Prerequisites: As identified by the GSE Frameworks
Length of Unit

10 Days
Right Triangle Trig.
Concept 1
Right Triangle Trig Review
GSE Standards
MGSE9‐12.G.SRT.6
Understand that by similarity, side ratios in
right triangles are properties of the angles in
the triangle, leading to definitions of
trigonometric ratios for acute angles. (Special
right triangles are included here.)
Concept 2
Concept 3
Unit Circle – Radians/Arc Length/Trig
Ratios
Co-terminal and Reference Angles
GSE Standards
GSE Standards
MGSE9‐12.F.TF.1
Understand radian measure of an angle as the
length of the arc on the unit circle subtended
by the angle.
MGSE9‐12.F.TF.2
Explain how the unit circle in the coordinate
plane enables the extension of trigonometric
functions to all real numbers, interpreted as radian
measures of angles traversed counterclockwise
around the unit circle.
MGSE9‐12.G.SRT.7
Explain and use the relationship between the
sine and cosine of complementary angles.
MGSE9‐12.G.SRT.8
Use trigonometric ratios and the Pythagorean
Theorem to solve right triangles in applied
problems.
Lesson Essential Question
What is the Pythagorean Theorem, and when
is this theorem used?
How are the sides and angles of right triangles
related to each other?
How can right triangle relationships be used
to solve practical problems?
TCSS
Lesson Essential Question
How do you find arc length of a circle?
How do you find radians?
9/11/2015
Lesson Essential Question
What are co- terminal and reference angles?
How do I find the co-terminal and reference
angles?
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TCSS – GSE Pre-Calculus – Unit 1
Vocabulary
30-60-90 Special Right Triangle
45-45-90 Special Right Triangle
Adjacent
Angle
Cosecant
Cosine
Cotangent
Hypotenuse
Opposite
Reciprocal Functions
Secant
Sine
Tangent
Vocabulary
Arc Length
Degrees
Odd/Even functions
Periodicity
Pi
Radians
Symmetry
Unit Circle
Arccosine
Arcsine
Arctangent
Decreasing
Domain
Increasing
Invertible function
Resources – Concept 1
Resources – Concept 2
 Trigonometry for any angle (Power
 Intro to converting degrees to
radians (Power Point)
 What is a Radian Discovery Task
 Angles and Radian Measure (guided
notes and practice )
KEY
 Unit Circle
Blank
Complete
 Degrees & Radians Conversion
Practice
 Intro to Trig Practice
 Intro to the Unit Circle (Power Point)
 Unit Circle Teacher Notes
 Practice (basics and the unit circle)
 Exact Trig Value Chart
 Unit Circle/Trig Practice KEY
 More Unit Circle Practice
Point)
 Right Triangle Trig Review notes
(guided notes and practice)
 Right Triangle Applications Review
(guided notes and practice)
 Trig Review Practice Worksheet
KEY
 Trig Cut Up Puzzle
Differentiated Activities
Concept 1
 Unit Guided Notes/
Vocabulary
Differentiated Activities
Concept 2
Resources – Concept 3
 Point on a Terminal Side Notes
 Graphic Organizer (culminating)
Differentiated Activities
Concept 3
 Differentiated Unit Circle Activity
Activities/Practice
(highly recommended)
TCSS
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TCSS – GSE Pre-Calculus – Unit 1
Unit 1 Checklist – Unit Circle-Trig Functions
Good luck to ________________________Date_______ Period___
Keep this list handy and refer to it periodically to see how you are doing. If you know how to each of these you should do well on
an exam.
Unit 1 – Unit Circle - Trig Functions self-assessment and tracker
In this unit I :
sort of
really
• can accurately complete the unit circle.
• can use the unit circle to find trig ratios for any degree or radian measure.
• can convert from degree to radian measure.
• can find arc length.
• can compute reference and co-terminal angles.
TCSS
9/11/2015
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