Math Ladder · High school · Grade 12

Precalculus and Trigonometry

Full trigonometry on the unit circle, identities, vectors, polar form, conic sections, sequences and a first look at limits.

0 of 61 topics passed

Start this course Skill map

61 topics in 9 units. Builds on Algebra 2. Leads to Calculus 1: Limits and Derivatives and Discrete Math. Not sure this is the right course? Find your rung.

  • Passed
  • Review due
  • Learning
  • Ready to learn
  • Needs an earlier topic

Unit 1 Angles and the Unit Circle

10 topics

Measure angles in radians and define sine and cosine for every angle.

  1. Angles in Standard Position
  2. Radian Measure
  3. Converting Degrees and Radians
  4. Arc Length, Sector Area and Angular Speed
  5. Sine and Cosine on the Unit Circle
  6. Exact Values at Special Angles
  7. Reference Angles and Signs by Quadrant
  8. Symmetry and Periodicity
  9. All Six Trig Functions
  10. The Pythagorean Identity

Unit 2 Graphs of Trig Functions

8 topics

Graph sinusoids, model periodic change, and define the inverse trig functions.

  1. Graphs of Sine and Cosine
  2. Amplitude and Period
  3. Phase Shift and Midline
  4. Modeling with Sinusoids
  5. Graphs of Tangent, Secant and Cosecant
  6. Damped Oscillation
  7. Inverse Trig Functions
  8. Compositions with Inverse Trig

Unit 3 Identities and Equations

7 topics

Prove identities, use sum and multiple-angle formulas, and solve trig equations.

  1. Reciprocal, Quotient and Pythagorean Identities
  2. Verifying Identities
  3. Sum and Difference Formulas
  4. Double-Angle Formulas
  5. Half-Angle and Power-Reducing Formulas
  6. Solving Basic Trig Equations
  7. Trig Equations with Factoring and Multiple Angles

Unit 4 Oblique Triangles and Vectors

9 topics

Handle the ambiguous case, then use vectors for forces and motion.

  1. The Ambiguous Case
  2. Bearings and Triangle Applications
  3. Heron's Formula
  4. Vectors
  5. Vector Components and Magnitude
  6. Adding and Scaling Vectors
  7. Velocity and Force Problems
  8. The Dot Product and the Angle Between Vectors
  9. Vector Projections and Work

Unit 5 Polar Coordinates and Complex Numbers

7 topics

Describe points and curves with polar coordinates, and multiply complex numbers as rotations.

  1. Polar Coordinates
  2. Converting Polar and Rectangular
  3. Graphs of Polar Equations
  4. Complex Numbers in the Plane
  5. Polar Form of a Complex Number
  6. Multiplying, Powers and De Moivre's Theorem
  7. nth Roots of Complex Numbers

Unit 6 Parametric Equations

3 topics

Describe motion with a parameter and eliminate it to find the path.

  1. Parametric Equations
  2. Eliminating the Parameter
  3. Projectile Motion with Parametric Equations

Unit 7 Conic Sections

4 topics

Write and graph parabolas, ellipses and hyperbolas, and identify a conic from its equation.

  1. Parabolas as Conics
  2. Ellipses
  3. Hyperbolas
  4. Identifying Conics from Equations

Unit 8 Matrices

7 topics

Add, multiply and invert matrices, and use them to solve systems and transform the plane.

  1. Matrices and Matrix Arithmetic
  2. Multiplying Matrices
  3. Solving Systems with Row Operations
  4. Determinants of 2 × 2 and 3 × 3 Matrices
  5. Inverse Matrices
  6. Solving Systems with Inverse Matrices
  7. Matrices as Transformations

Unit 9 Toward Calculus

6 topics

Decompose fractions, prove by induction, and meet difference quotients and limits.

  1. Partial Fraction Decomposition
  2. Proof by Induction
  3. Logistic Growth
  4. The Difference Quotient
  5. The Idea of a Limit
  6. Estimating Limits from Graphs and Tables
@teddyrookbook GitHub