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Mathematics · Grade 11

Trigonometric Functions and Periodic Models

Learners extend trigonometry from right triangles to all angles. They measure angles in radians, use the unit circle to evaluate sine, cosine and tangent of any angle, prove the Pythagorean identity sin^2^θ + cos^2^θ = 1, graph sinusoidal functions with amplitude, period, midline and phase shift, and model Ferris wheels, tides and daylight hours with invented but realistic data.

  • 4 lessons
  • About 135 minutes
  • Trigonometric functions check: 11 questions
  • Ways to answer: choose an answer, match pairs, type a number, put in order, sort into groups and write a short answer
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What learners will discover

  • Explain radian measure as arc length on the unit circle and convert between degrees and radians.
  • Evaluate sine, cosine and tangent of any angle with the unit circle, reference angles and quadrant signs, and prove and apply the Pythagorean identity.
  • Graph and interpret sinusoidal functions, identifying amplitude, period, midline and phase shift, and describe the graph of tangent.
  • Model periodic phenomena with sinusoidal functions and interpret the parameters in context.

Lessons

  1. Radian measure 5 steps3 practiceabout 28 min
  2. The unit circle and the Pythagorean identity 6 steps4 practiceabout 35 min
  3. Graphs of sinusoidal functions 6 steps4 practiceabout 35 min
  4. Periodic models 6 steps3 practiceabout 32 min
  5. Trigonometric functions check 11 questions at the end

Keep exploring

More 11th grade math

Guide for grown-ups