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Level 1 · 41 lessons

Algebra and Geometry II: Trigonometry, Complex Numbers and Geometry of Space

Trigonometry, complex numbers, matrices and analytic geometry of space.

Course content

Unit 0Course overview

  1. 01Syllabus of Algebra and Geometry II

Unit 1Trigonometric functions and polar coordinates

  1. 02Trigonometric functions and polar coordinates: introduction
  2. 03Angles and their measure: degrees and radians
  3. 04Trigonometric ratios and the unit circleWith account
  4. 05The trigonometric functions and their graphsWith account
  5. 06The inverse trigonometric functionsWith account
  6. 07Solving triangles: the laws of sines and cosinesWith account
  7. 08Polar coordinates and polar curvesWith account
  8. 09Trigonometry and polar coordinates: synthesis and challengesWith account

Unit 2Analytic trigonometry

  1. 10Analytic trigonometry: introductionSubscriptionWith account
  2. 11Fundamental trigonometric identitiesSubscriptionWith account
  3. 12Sum and difference formulas, double angle and half angleSubscriptionWith account
  4. 13Sum-to-product formulas and the harmonic formSubscriptionWith account
  5. 14Trigonometric equations and inequalitiesSubscriptionWith account
  6. 15The angle between two lines and applications of trigonometrySubscriptionWith account
  7. 16Rotation of axes and the general second-degree equationSubscriptionWith account
  8. 17Analytic trigonometry: synthesis and challengesSubscriptionWith account

Unit 3Complex numbers in polar form

  1. 18Complex numbers in polar form: introductionSubscriptionWith account
  2. 19The polar form of complex numbersSubscriptionWith account
  3. 20De Moivre’s formula and powers of complex numbersSubscriptionWith account
  4. 21The nth roots of a complex number and the roots of unitySubscriptionWith account
  5. 22The complex exponential and Euler’s formulaSubscriptionWith account
  6. 23Geometry with complex numbersSubscriptionWith account
  7. 24Complex polynomial equations: the Cardano and Ferrari formulasSubscriptionWith account
  8. 25Complex numbers in polar form: synthesis and challengesSubscriptionWith account

Unit 4Matrices and algebraic structures

  1. 26Matrices and algebraic structures: introductionSubscriptionWith account
  2. 27Matrices and matrix operationsSubscriptionWith account
  3. 28Linear systems and the Gauss-Jordan methodSubscriptionWith account
  4. 29Determinants: properties and Cramer’s ruleSubscriptionWith account
  5. 30The inverse matrixSubscriptionWith account
  6. 31Matrices as transformations of the planeSubscriptionWith account
  7. 32Complex numbers as matricesSubscriptionWith account
  8. 33Algebraic structures: groups, rings and fieldsSubscriptionWith account
  9. 34Matrices and algebraic structures: synthesis and challengesSubscriptionWith account

Unit 5Analytic geometry of space

  1. 35Analytic geometry of space: introductionSubscriptionWith account
  2. 36Vectors in space and the dot productSubscriptionWith account
  3. 37The cross product and the scalar triple productSubscriptionWith account
  4. 38Lines and planes in spaceSubscriptionWith account
  5. 39Distances, angles and volumes in spaceSubscriptionWith account
  6. 40Analytic geometry of space: synthesis and challengesSubscriptionWith account

Unit 6Course closing

  1. 41Final review of Algebra and Geometry IISubscriptionWith account