Trigonometry | Index

Trigonometry studies the functions that connect angles to lengths: sine, cosine, tangent and their reciprocals.

The course covers radians, the unit circle and trig graphs. It also covers inverse trig functions, identities, equations, the laws of sines and cosines, and polar coordinates.

It’s for high school trigonometry and precalculus students, college trigonometry students and anyone preparing for calculus.

What to know first: Algebra 2, plus the right triangle lessons in Geometry, Unit 9.

Every lesson in this course is live. The list below shows them all in teaching order.

Units in this course

Unit 1: Angles and Radian Measure

  1. Angles in Standard Position — initial and terminal sides, and positive and negative angles
  2. Coterminal Angles — find angles that share a terminal side
  3. Radians — what a radian is and how to convert between degrees and radians
  4. Linear and Angular Speed — relate how fast a point moves around a circle to how fast its angle changes

Also see: arc length and the area of a sector in Geometry, Unit 10.

Unit 2: Right Triangle Trigonometry

  1. Six Trigonometric Functions — sine, cosine, tangent and their reciprocals cosecant, secant and cotangent
  2. Trig Values of Special Angles — exact trig values for 30, 45 and 60 degree angles

Also see: the Pythagorean theorem, trigonometric ratios and solving right triangles in Geometry, Unit 9.

Unit 3: The Unit Circle and Trig Functions of Any Angle

  1. Trig Functions of Any Angle — use a point on the terminal side to find all six trig values
  2. Reference Angles — find reference angles and use the sign of each function in each quadrant
  3. The Unit Circle — exact sine and cosine values for common angles in degrees and radians

Unit 4: Graphs of Trig Functions

  1. Parent Functions — review the graphs, domains and ranges of the basic function families
  2. Graphs of Sine and Cosine — the shape, key points and period of the sine and cosine graphs
  3. Amplitude and Period — find the amplitude and period from an equation or a graph
  4. Phase Shift — shift sine and cosine graphs left, right, up and down
  5. Graph of Tangent — the shape, period and asymptotes of the tangent graph
  6. Graphs of Secant, Cosecant and Cotangent — graph the reciprocal trig functions
  7. Sinusoidal Models — model repeating patterns like tides and Ferris wheels

Unit 5: Inverse Trig Functions

  1. Inverse Trig Functions — arcsine, arccosine and arctangent and their restricted ranges
  2. Compositions of Inverse Trig Functions — evaluate a trig function of an inverse trig function

Unit 6: Trig Identities

  1. Fundamental Trig Identities — the reciprocal, quotient and Pythagorean identities
  2. Verifying Trig Identities — prove an identity by rewriting one side until it matches the other
  3. Sum and Difference Formulas — find exact values for sums and differences of angles
  4. Double-Angle Formulas — rewrite trig functions of twice an angle
  5. Half-Angle Formulas — find exact values for half of an angle

Unit 7: Trig Equations

  1. Solving Trig Equations — find all solutions on an interval and the general solution
  2. Trig Equations with Multiple Angles — solve equations like sine of 2x when the angle is multiplied
  3. Solving Trig Equations with Identities — use identities and factoring to solve harder equations

Unit 8: Law of Sines and Law of Cosines

  1. Law of Sines — solve triangles that aren’t right triangles using sine ratios
  2. Ambiguous Case of the Law of Sines — decide whether two sides and an angle give zero, one or two triangles
  3. Law of Cosines — solve triangles when you know three sides or two sides and the angle between
  4. Area of Oblique Triangles — find a triangle’s area with the sine formula or Heron’s formula

Unit 9: Polar Coordinates and Complex Numbers

  1. Polar Coordinates — plot points and convert between polar and rectangular coordinates
  2. Graphing Polar Equations — graph circles, roses, cardioids and limaçons
  3. Trigonometric Form of Complex Numbers — write complex numbers with a modulus and angle, then multiply and divide
  4. De Moivre’s Theorem — find powers and roots of complex numbers

For Teachers: Standards Alignment

Lessons cover the Common Core trig function standards (F-TF), the laws of sines and cosines (G-SRT), and the trig and polar topics in AP Precalculus Unit 3. Right triangle basics are taught in Geometry. Vectors and parametric equations are taught in Precalculus.

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