MATH ANALYSIS A
UNIT 1: THE SIX TRIGONOMETRIC FUNCTIONS
1.1
1.2
1.3
1.4
1.5
Angles, Degrees, and Special Triangles
The Rectangular Coordinate System
Definition1: Trigonometric Functions
Introduction to Identities
More Identities
Standards:
Students understand the notion of angle and how to measure it, in both degree and
radians; they can convert between degrees and radians.
TR 2.0
Students know the definition of sine and cosine as y and x coordinates of points on the
unit circle and are familiar with the graphs of sine and cosine functions.
TR 3.0
Students know the identity 𝑠𝑖𝑛2 𝑥 + 𝑐𝑜𝑠 2 𝑥 = 1 -- prove the identity using the Pythagorean
Theorem and prove other trigonometric identities
TR 9.0
Students will prove the addition and subtraction formulas for sine, cosine, and
tangent and use them to solve problems
TR 5.0
Students know the definitions of tangent and cotangent functions
TR 6.0
Students know the definitions of secant and cosecant functions
TR 5.0
Students know the definitions of tangent and cotangent functions
TR 6.0
Students know the definitions of secant and cosecant functions
TR 12.0
Students use trigonometry to determine unknown sides or angles in right triangles
TR 19.0
Students are adept at using trigonometry in a variety of applications and word problems
TR 1.0
UNIT 2: RIGHT TRIANGLE TRIGONOMETRY
2.1
2.2
2.3
2.4
Definition 11: Right Triangle Trigonometry
Calculators and Trigonometric Functions of Acute Angle
Solving Right Triangles
Applications
Standards:
TR 5.0
TR 6.0
TR 12.0
TR 19.0
TR 9.0
Students know the definitions of tangent and cotangent functions
Students know the definitions of secant and cosecant functions
Students use trigonometry to determine unknown sides or angles in right triangles
Students are adept at using trigonometry in a variety of applications and word problems
Students can compute the values of trigonometric functions and the inverse
trigonometric functions at various standard points.
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UNIT 3: RADIAN MEASURE
3.1
3.2
3.3
3.4
3.5
Reference Angle
Radians and Degrees
Definition III: Circular Functions
Arc Length and Area of a Sector
Velocities
Standards:
T-TF
1.0
T-TF
2.0
T-TFF
3.0
TR 1.0
TR 1.0
TR 2.0
TR 3.0
Understand radian measure of an angle as the length of the arc on the unit circle
subtended by the angle.
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.
(+) Use special triangles to determine geometrically the values of sine,cosine, tangent for
π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosine, and
tangent for π–x, π+x, and 2π–x in terms of their values for x, where x is any real number.
Students understand the notion of angle and how to measure it, in both degree and
radians; they can convert between degrees and radians.
Students understand the notion of angle and how to measure it, in both degree and
radians; they can convert between degrees and radians.
Students know the definition of sine and cosine as y and x coordinates of points on the
unit circle and are familiar with the graphs of sine and cosine functions.
Students know the identity 𝑠𝑖𝑛2 𝑥 + 𝑐𝑜𝑠 2 𝑥 = 1 -- prove the identity using the Pythagorean
Theorem and prove other trigonometric `identities
UNIT 4: GRAPHING AND INVERSE FUNCTIONS
4.1
4.2
4.3
4.4
4.5
4.6
Basic Graphs
Amplitude and Period
Phase Shift
Finding and Equation from its Graph
Graphing Combinations of Functions
Inverse Trigonometric Functions
Standards:
TR 4.0
Students graph functions of the form 𝑓(𝑡) = 𝐴𝑠𝑖𝑛(𝐵𝑡 + 𝐶) or 𝑓(𝑡) = 𝐴𝑐𝑜𝑠(𝐵𝑡 + 𝐶) and
interpret A, B, and C in terms of amplitude, frequency, period and phase shift.
TR 5.0
Students know the definitions of tangent and cotangent functions
TR 6.0
Students know the definitions of secant and cosecant functions
TR 7.0
Students know that the tangent of the angle that a line makes with the x-axis is equal to
the slope of the line.
TR 8.0
Students know the definition of inverse trigonometric functions and can graph the
functions.
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UNIT 5: IDENTITIES AND FORMULAS
5.1
5.2
5.3
5.4
5.5
Proving Identities
Sum and Difference Formulas
Double-Angle Formulas
Half-Angle Formulas
Additional Formulas
Standards:
TR 9.0
TR 10.0
TR 11.0
TR 19.0
Students can compute the values of trigonometric functions and the inverse
trigonometric functions at various standard points.
Students demonstrate an understanding of the addition formulas for sines and cosines
and their proofs and can use those formulas to prove and/or simplify other trigonometric
identities
Students demonstrate an understanding of half-angle and double-angle formulas for sines
and cosines and can use those formulas to prove and/or simplify other trigonometric
identities
Students are adept at using trigonometry in a variety of applications and word problems
UNIT 6: EQUATIONS
6.1
6.2
6.3
6.4
Solving Trigonometric Equations
More on Trigonometric Equations
Trigonometric Equations Involving Multiple Angles
Parametric Equations and Further Graphing
Standards:
T-TF
7.0
MA 1.0
TR 9.0
TR 12.0
TR 19.0
Use inverse functions to solve trigonometric equations that arise in modeling contexts;
evaluate the solutions using technology, and interpret them in terms of the context.
interpret them in terms of the context.★
Students are familiar with, and can apply, polar coordinates and vectors in the plane. In
particular, they can translate between polar and rectangular coordinates and can
interpret polar coordinates and vectors graphically.
Students can compute the values of trigonometric functions and the inverse
trigonometric functions at various standard points.
Students use trigonometry to determine unknown sides or angles in right triangles
Students are adept at using trigonometry in a variety of applications and word problems
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UNIT 7: TRIANGLES
7.1
7.2
7.3
7.4
7.5
The Law of Sines
The Ambiguous Case
The Law of Cosines
The Area of a Triangle
Vectors: An Algebraic Approach
Standards:
TR 13.0
TR 14.0
MA 1.0
LA 7.0
LA 12.0
Students know the Law of Sines and the Law of Cosines and apply those laws to solve
problems.
Students know the area of a triangle, given one angle and two adjacent sides.
Students are familiar with, and can apply, polar coordinates and vectors in the plane. In
particular, they can translate between polar and rectangular coordinates and can
interpret polar coordinates and vectors graphically.
Students demonstrate an understanding of the geometric interpretation of vectors and
vector addition (by means of parallelograms) in the plane and in three dimensional space
Students compute the scalar (dot) product of two vectors in n-dimensional space and know
that perpendicular vectors have zero dot product
Math Analysis A, Fall Semester 2013
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