Lafayette Parish School System
Advanced Math Pre-Calculus Curriculum Map
Unit 4: Trigonometry of Triangles
Time Frame:
CC #
Common Core
Evidence / Assessments of learning
Instructional
Notes/Strategies
Differentiation
Student Understandings
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The Law of sines
The Law of cosines
Solving of a triangle Using the Law of cosines
Applications using the Law of sines and cosines
G.SRT.10
Prove the Law of Sines and Cosines and use
them to solve problems.
G.SRT.11
Understand and apply the Law of Sines and
Cosines to find unknown measurements in
right and non-right triangles.
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Supplementary Angle Identity
Area of a Triangle Using the Law of sines
Heron’s Formula
The Complex Plane
Polar Form of Complex numbers
Demoivre’s Theorem
Solve oblique triangles using the Law of
Sines
Solve real world problems using the Law of
Sines
Solving of Triangles using the Law of
Cosines
Applications of the Law of Cosines
Solve real world problems using the Law of
Sines
Supplementary Angle Identitiy
When is it necessary to use the Law of Sines to
solve a triangle? When is it necessary to use the
Law of Cosines to solve a triangle?
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Formulas and rules for the nth root of
complex numbers
Vectors in a plane
Properties of Vectors
Applications of Vectors in a plane
The Dot Product
Properties of the Dot Product
7.2 Law of Sines
7.3 Law of Cosines
NCTM Illuminations Activity
Trigonometric Identities, Equations,
and Applications (pages 28-31 Law of
Sines, Cosines, and Area)
Regents Prep: Laws of Sines &
Cosines
Math Tools: various oblique triangle
resources
Wolfram Interactive Demo: Solving
Oblique Triangles
Math Warehouse: Law of Sines
Math Warehouse: Law of Sines
Ambiguous Case
Math Warehouse: Law of Cosines
Illustrative Math Task: Law of
Cosines: Satellite
Illustrative Math Task: Law of
Cosines: Lighthouse
Lafayette Parish School System
Advanced Math Pre-Calculus Curriculum Map
Unit 4: Trigonometry of Triangles
Time Frame:
CC #
Common Core
Evidence / Assessments of learning
Instructional
Notes/Strategies
Differentiation
Discovery Education Streaming
Videos (search: Law of Sines or Law
of Cosines)
G.SRT.9
1
ab sin(c) for the
2
area of a triangle by drawing an auxiliary line
from a vertex perpendicular to the opposite
side
Derive the formula A 
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Find area of oblique triangles
7.4 Area of a
Triangle
Can students find the areas of oblique triangles?
Math TV (Select:
Trigonometry>Triangles>The Area
of a Triangle)
eHow Video: How to Find Area of an
Oblique Triangle
Math is Fun: Area of Triangles
without Right Angles
N.CN.4
N.CN.5
N.CN.3
N.VM.1
N.VM.2
Represent complex numbers on the complex
plane in rectangular and polar form (including
real and Imaginary numbers) and explain
why the rectangular and polar forms of given
complex numbers represent the same number.
Represent addition, subtraction,
multiplication, and conjugation of complex
numbers geometrically on
the complex plane; use properties of this
representation for computation.
Find the conjugate of a complex number; use
conjugates to find moduli and quotients of
complex numbers.
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Recognize vector quantities as having both
magnitude and direction. Represent vector
quantities by directed line segments and use
appropriate symbols for vectors and their
magnitudes.
Find the components of a vector by
subtracting the coordinates of an initial point
from the coordinates of a terminal point.
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Graph a complex number in the complex
plane
Express a complex number in polar form
Perform polar multiplication and division
Calculate power and roots of complex
numbers
8.3 The Complex
Plane; De Moivre’s
Theorem
ck-12 Foundation: Derivation of the
Triangle Area Formula
Math Warehouse: Graphing
Complex Numbers in Complex Plane
Regents Prep: Representing Complex
Numbers Graphically
ck-12 Foundation: Polar Form of
Complex Numbers
How is a complex number converted to polar
form?
TI NSpire CX Activity: Complex
Numbers: Plotting and Polar Form
Note: Cover N.CN.6 as an extension if time
permits. (Additional resources required-not in text)
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Find the components and magnitude of a
vector
Add and subtract vectors
Perform scalar multiplication of vectors
Determine the direction angle of a vector
Find the dot product of two vectors and the
angle between two vectors
8.4 Vectors
8.5 The Dot
Product
Math is Fun: Vectors
Math TV (Select:
Trigonometry>Triangles>Vectors:An
Algebraic Approach)
Math is Fun: Dot Product
Lafayette Parish School System
Advanced Math Pre-Calculus Curriculum Map
Unit 4: Trigonometry of Triangles
Time Frame:
CC #
N.VM.3
N.VM.4A
N.VM.4B
N.VM.4C
N.VM.5A
N.VM.5B
Common Core
Solve problems involving velocity and the
other quantities that can be represented by
vectors.
Add vectors end-to-end, component wise, and
by the parallelogram rule. Understand that the
magnitude of a sum of two vectors is typically
not the sum of the magnitudes.
Given two vectors in magnitude and direction
form, determine the magnitude and direction
of their sum.
Understand vector subtraction v-w as v + (w), where (-w) is the additive inverse of w,
with the same magnitude as w and pointing in
the opposite direction. Represent vector
subtraction graphically by connecting the tips
in the appropriate order, and perform vector
subtraction component wise.
Represent scalar multiplication graphically by
scaling vectors and possibly reversing their
direction; perform scalar multiplication
component-wise.
Compute the magnitude of a scalar multiple
cv by using cv  c v . Compute the direction
of cv knowing that when c v  0 ,the
direction of cv is either along v (for c > 0) or
against v (for c < 0).
Evidence / Assessments of learning
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Determine the projection and component
vectors and use them in physical applications
What is the difference between vectors and rays?
Instructional
Notes/Strategies
Differentiation
University of Tennessee: Interactive
tutorial:vectors
PhET Simulator: Vector Addition