Trigonometry: Math 112
Chapter 6: Trigonometric Functions
6.1 Angles and Their Measure
Convert between decimals and degrees, minutes, seconds forms for angles
Find the arc length of a circle
Convert from degrees to radians and from radians to degrees
Find the area of a sector of a circle
Find the linear speed of an object travelling in circular motion
6.2 Trigonometric Functions: Unit Circle Approach
Find the exact values of the trigonometric functions using a point on the unit circle
Find the exact values of the trigonometric functions of quadrilateral angles
Find the exact values of the trigonometric functions for integer multiples of pi/6=30degrees, pi/4=45degrees, and pi/3=60degrees
Use a calculator to approximate the value of a trigonometric function
Use a circle radius r to evaluate the trigonometric functions
6.3 Properties of the Trigonometric Functions
Determine the Domain and The Range of the Trigonometric functions
Determine the Period of the Trigonometric Functions
Determine the Signs of the Trigonometric Functions in a Given Quadrant
Find the Values of the Trigonometric Functions Using Fundamental Identities
Use Even-Odd Properties to Find the Exact Values of the Trigonometric Functions 1
Use Even-Odd Properties to Find the Exact Values of the Trigonometric Functions 2
Using periodic properties to evaluate trig functions without a calculator
6.4 Graphs of the Sine and Cosine Functions
Graph Functions of the Form y=Asin(wx) and y=Acos(wx) Using Transformations
Determine the Amplitude and Period of Sinusoidal Functions
Chapter 7: Analytic Trigonometry
7.1 The Inverse sine, cosine, and tangent functions
Find the exact value of an inverse sine, cosine, or tangent function
Find an approximate value of an inverse sine function
Find the inverse function of a trigonometric function
Solve equations involving inverse trigonometric functions
7.2 The Inverse Trigonometric Functions (cont'd)
Find the exact value of expressions involving the inverse sine, cosine, and tangent functions
Know the definitions of the inverse secant, cosecant, and cotangent functions
Use a calculator to evaluate sec -1x, csc-1x, and cot-1x
7.3 Trigonometric Identities
Use algebra to simplify trigonometric expressions
7.4 Sum and Difference Formulas
Use sum and difference formulas to find exact values
Use " " to establish identities
Use " " involving inverse trigonometric functions
7.5 Double-angle and Half-angle Formulas
Use double –angle formulas to find exact values
7.6 Product-to-Sum and Sum-to-Product Formulas
Express products as sums and sums as products
7.7 Trigonometric Equations
Solve equations involving a single trigonometric function
7.8 Trigonometric Equations II
Solve trigonometric equations quadratic in form
Solve trigonometric equations using identities
Chapter 8: Applications of Trigonometric Functions
8.1 Right Triangle Trigonometry; Applications
Find the value of trigonometric functions of acute angles using right triangles
Use the complimentary angle theorem
8.2 The Law of Sines
8.3 The Law of Cosines
8.5 Simple Harmonic Motion; Damped Motion; Combining Waves
Build a model for an object in simple harmonic motion
Analyze a simple harmonic motion
Analyze an object in damped motion
Chapter 9: Polar Coordinates; Vectors
9.2 Polar Equations and Graphs
Graph and identify polar equations by converting to rectangular equations
Graph polar equations using a graphing utility
9.3 The Complex Plane; De Moivre's Theorem
Convert a complex number from rectangular form to polar form
Find products and quotients of complex numbers in polar form
9.4 Vectors
Add and subtract vectors algebraically
Find a scalar multiple and the magnitude of a vector
Find a vector from its direction and magnitude
9.5 The Dot Product ( . X .= . )
Find the dot product of two vectors
Find the angle between two vectors
Determine whether two vectors are parallel
Determine whether vectors are orthogonal
9.6 Vectors in Space!!!!
Perform operations on vectors
Find the angle between two vectors
Find the direction angles of a vector
9.7 The Cross Product
Find the cross product of two vectors
Know algebraic properties of the cross product
Know geometric properties of the cross product
Find a vector orthogonal to two given vectors
10: Analytic Geometry
10.1 Conics
10.2 The Parabola
Analyze parabolas with vertex at the origin
Analyze parabolas with vertex at (h,k)
10.3 The Ellipse
Analyze ellipses with center at the origin
Analyze ellipses with center at (h,k)
10.4 The Hyperbola
Analyze hyperbolas with center at origin
Find the asymptotes of a hyperbola
10.5 Rotation of Axes; General form of a conic
Identify a conic
Use a rotation of axes to transform equations
Analyze an equation using a rotation of axes
10.6 Polar Equations of Conics
Analyze and graph polar equations of conics
Convert the polar equation of a conic to a rectangular equation
10.7 Plane Curves and Parametric Equations
Graph parametric equations by hand
Graph parametric equations using a graphing utility
Find a rectangular equation for a curve defined parametrically