The Pre-Cal Course builds on the students' mathematical understanding of algebra and geometry as well as deepens the student’s mathematical fluency. This course introduces new concepts such as trigonometry, vectors, and polar equations. Pre-Cal Topics include: (1) Angles and Unit Circle Trigonometry, (2) Graphing Trigonometric Functions, (3) Trigonometric Identities and Formulas, (4) Solving Trigonometric Equations, (5) Right Triangle Trigonometry, (6) Vectors, and (7) Parametric and Polar Equations.

- Introduction to Angles in Trigonometry
- Standard Position of an Angle
- Angles Measured in Degrees
- Angles Measured in Degrees, Minutes, and Seconds
- Angles Measured in Radians
- Coterminal Angles
- Converting Degrees to Radians and Radians to Degrees
- Common Angles in Degrees and Radians
- Finding the Arc Length of a Circle
- Finding the Area of a Sector
- Finding the Linear and Angular Speed in Circular Motion
- Finding the Distance Between Two Cities

- The Unit Circle
- Creating the Unit Circle
- Finding Trigonometric Values Using the Unit Circle
- Finding Trigonometric Values of Quadrant Angles Using the Unit Circle
- Trigonometric Values of Common Angles
- Evaluating Trigonometric Expressions
- Using a Circle with Radius r to Evaluate Trigonometric Values
- Trigonometric Signs in Different Quadrants
- Finding All Six Trigonometric Values Given Sine and Cosine Values
- Finding All Six Trigonometric Values Given One (x,y) Point
- Finding All Six Trigonometric Values Given One and the Sign of Another
- Reference Angles
- Finding Trigonometric Values Using Reference Angles

- Introduction to Sinusoidal Graphs
- Basic Sine and Cosine Graphs
- The Amplitude of Sine and Cosine Graphs
- The Period of Sine and Cosine Graphs
- Horizontal Phase Shifts (Translations) of Sine and Cosine Graphs
- Vertical Phase Shifts (Translations) of Sine and Cosine Graphs
- Determining the Equation of a Sinusoidal Graph
- Graphing Tangent Functions
- Graphing Cotangent Functions
- Graphing Cosecant and Secant Functions
- Simple Harmonic Motion

- Inverse Sine Function
- Composition of Sine and Inverse Sine Functions
- Inverse Cosine Function
- Composition of Cosine and Inverse Cosine Functions
- Inverse Tangent Function
- Composition of Tangent and Inverse Tangent Functions
- Composition of Inverse Functions (Sine, Cosine, Tangent)
- Inverse Cosecant, Inverse Secant, and Inverse Cotangent
- Composition of Inverse Functions (Cosecant, Secant, and Cotangent)
- Using a Calculator to Evaluate Inverse Cosecant, Inverse Secant, and Inverse Cotangent Expressions

- Reciprocal, Quotient, and Pythagorean Identities
- Simplifying Expressions with the Reciprocal, Quotient, and Pythagorean Identities
- Proving Identities with the Reciprocal, Quotient, and Pythagorean Identities
- Even and Odd Identities
- Proving More Trigonometric Identities
- Factoring and FOILing to Prove Trigonometric Identities

- Sum and Difference Sine Formulas (Finding Exact Values)
- Sum and Difference Cosine Formulas (Finding Exact Values)
- Sum and Difference Tangent Formulas (Finding Exact Values)
- Using Sum and Difference Formulas
- Using Sum and Difference Formulas with Inverse Functions
- Proving Identities Using Sum and Difference Formulas
- Double Angle Sine Formula
- Double Angle Cosine Formulas
- Double Angle Tangent Formulas
- Power-Reducing Formulas
- Half-Angle Sine Formula
- Half-Angle Cosine Formula
- Half-Angle Tangent Formula
- Using Double Angle and Half Angle Formulas with Inverse Functions
- Product-to-Sum Formulas
- Sum-to-Product Formulas

- Using Reference Angles to Solve Trigonometric Equations
- Finding All Solutions of Trigonometric Equations
- Solving Basic Trigonometric Equations
- Solving Trigonometric Equations by Combining Like Terms
- Solving Trigonometric Equations by Taking the Square Root
- Solving Trigonometric Equations by Factoring
- Solving Trigonometric Equations with an Argument of 2?¸
- Solving Trigonometric Equations with an Argument of ?/2
- Solving Trigonometric Equations with an Argument Expression
- Solving Trigonometric Equations Using Identities

- Right Triangle Trig Ratios
- Complementary Angle Theorem with Trigonometry
- Solving Word Problems Using Right Triangle Trigonometry
- Law of Sines
- The Ambiguous Case for the Law of Sines
- Trigonometry Fomula for the Area of a Triangle
- Law of Cosines
- Heron's Formula for the Area of a Triangle
- Finding the Area of Quadrilaterals
- Navigation Problems (Direction and Bearing)

- Introduction to Vectors
- Properties of Adding Vectors
- The Negation of a Vector and Subtracting Vectors
- Scalar Multiplication with Vectors
- Vectors in Standard Position and Finding Position Vectors
- Vectors in Component Form
- Operations with Vectors in Component Form
- Magnitude of Vectors in Component Form
- Finding the Direction of a Vector in Component Form
- The Unit Vector in the Same Direction as v = (a,b)
- Vectors in ai + bj Form
- Operations with Vectors in ai + bj Form
- Magnitude of Vectors in ai + bj Form
- Finding the Direction of a Vector in ai + bj Form
- The Unit Vector in the Same Direction as v = ai + bj
- Finding the Horizontal and Vertical Components of a Vector
- The Dot Product of Two Vectors
- Finding the Angle Between Two Vectors
- Parallel Vectors
- Perpendicular (Orthogonal) Vectors

- Definition of Polar Coordinates and Plotting Polar Coordinates
- Plotting Polar Coordinates on a Polar Grid
- Finding Different Polar Coordinates for Same Point
- Converting Polar Coordinates to Rectangular Coordinates
- Converting Rectangular Coordinates to Polar Coordinates
- Transforming an Equation from Polar Form to Rectangular Form
- Transforming an Equation from Rectangular Form to Polar Form
- Graphing Polar Equations