Math 1022 College Trigonometry provides an in-depth treatment of functions and graphs; inverse trigonometric functions; fundamental identities and angle formulas; solving equations; triangles with applications; polar coordinate system.
Topics and Objectives
An Introduction to Angles: Degree and Radian Measure
Understanding degree measure and radian measure
Converting between degree measure and radian measure
Finding coterminal angles using degree measure and radian measure
Applications of Radian Measure
Determining the area of a sector of a circle
Determining the arc length of a sector of a circle
Triangles (Review)
Classifying triangles
Using the Pythagorean Theorem
Understanding similar triangles
Understanding the special right triangles
Right Triangle Trigonometry
Understanding the right triangle definitions of the trigonometric functions
Using the special right triangles
Understanding the fundamental trigonometric identities
Understanding cofunctions
Evaluating trigonometric functions using a calculator
Trigonometric Functions of General Angles
Understanding the four families of special angles
Understanding the definitions of the trigonometric functions of general angles
Finding the values of the trigonometric functions of quadrantal angles
Understanding the signs of the trigonometric functions
Determining reference angles
Evaluating trigonometric functions of angles belonging to the $\frac{\pi}{3}$, $\frac{\pi}{4}$, and $\frac{\pi}{6}$ families
The Unit Circle
Understanding the definition of the unit circle
Understanding the unit circle definitions of the trigonometric functions
The Graphs of the Trigonometric Functions
Understanding the graphs of the sine, cosine, tangent, cotangent, secant, and cosecant functions and their properties
Sketching graphs of the form $y=A\sin(Bx-C)+D$ or $y=A\cos(Bx-C)+D$
Sketching graphs of the form $y=A\tan(Bx-C)+D$ or $y=A\cot(Bx-C)+D$
Sketching graphs of the form $y=A\sec(Bx-C)+D$ or $y=A\csc(Bx-C)+D$
Determine the equation of a function of the form $y=A\sin(Bx-C)$ or $y=A\cos(Bx-C)$ given its graph
Inverse Trigonometric Functions
Understanding and finding the exact and approximate values of the inverse sine function, the inverse cosine function, and the inverse tangent function
Evaluating composite functions involving inverse trigonometric functions of the forms $f∘f^{-1}$, $f^{-1}∘f$, $f∘g^{-1}$, and $f^{-1}∘g$
Trigonometric Identities
Substituting known identities to verify an identity
Changing to sines and cosines to verify an identity
Factoring to verify an identity
Separating a single quotient into multiple quotients to verify an identity
Combining fractional expressions to verify an identity
Multiplying by conjugates to verify an identity
The Sum and Difference Formulas
Understanding and using the sum and difference formulas for the cosine, sine, and tangent functions
Using the sum and difference formulas to verify identities
Using the sum and difference formulas to evaluate expressions involving inverse trigonometric functions
The Double-Angle and Half-Angle Formulas
Understanding and using the double-angle formulas and the half-angle formulas
Using the double-angle and half-angle formulas to verify identities
Using the double-angle and half-angle formulas to evaluate expressions involving inverse trigonometric functions
Trigonometric Equations
Solving trigonometric equations that are linear or quadratic in form
Solving trigonometric equations using identities
Solving other types of trigonometric equations
Solving trigonometric equations using a calculator
Right Triangle Applications
Solving right triangles
Solving applications using right triangles
The Law of Sines
Determining if the Law of Sines can be used to solve an oblique triangle
Using the Law of Sines to solve the SAA case or the ASA case
Using the Law of Sines to solve the SSA (Ambiguous) case
Using the Law of Sines to solve applied problems involving oblique triangles
The Law of Cosines
Determining if the Law of Cosines can be used to solve an oblique triangle
Using the Law of Cosines to solve the SAS case
Using the Law of Cosines to solve the SSS case
Using the Law of Cosines to solve applied problems involving oblique triangles
Area of Triangles
Determining the area of oblique triangles
Using Heron’s Formula to determine the area of an SSS triangle
Solving applied problems involving the area of triangles
Polar Coordinates and Polar Equations
Plotting points using polar coordinates
Determining different representations of a point (r, θ)
Converting points from polar to rectangular coordinates and from rectangular to polar coordinates
Converting equations from rectangular to polar form and from polar to rectangular form
Graphing Polar Equations
Sketching equations of the form $r\cosθ = a$, $r\sinθ = a$, $ar\cosθ + br\sinθ = c$, and $θ = α$
Sketching equations of the form $r = a$, $r = a\sinθ$, and $r = a\cosθ$
Sketching equations of the form $r = a + b\sinθ$ and $r = a + b\cosθ$
Sketching equations of the form $r = a\sin(nθ)$ and $r = a\cos(nθ)$
Sketching equations of the form $r^{2} = a^{2}\sin(2θ)$ and $r^{2} = a^{2}\cos(2θ)$
Vectors
Understanding the geometric representation of a vector
Understanding operations on vectors represented geometrically
Understanding vectors in terms of components
Understanding vectors in terms of i and j
Finding a unit vector
Determining the direction angle of a vector
Representing a vector in terms of i and j given its magnitude and direction angle
Using vectors to solve applied problems involving velocity
Syllabus & Pacing Guide
Math 1022 College Trigonometry Syllabus & Pacing Guide