🎯
Learning Goal
Part of: Extend the domain of trigonometric functions using the unit circle — 4 of 4 cluster items
Explain symmetry and periodicity
HSF.TF.A.4
**HSF.TF.A.4**: (+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.
Show moreShow less
HSF.TF.A.4: (+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.
What you'll learn
- Explain why cosine is an even function (cos(-x) = cos(x)) using reflection across the x-axis on the unit circle
- Explain why sine is an odd function (sin(-x) = -sin(x)) using reflection across the x-axis on the unit circle
- Classify tangent as an odd function and justify using tan = sin/cos
- Demonstrate that sin and cos have period 2pi by showing that angles differing by 2pi have the same terminal point
- Demonstrate that tangent has period pi and explain why geometrically
- Use symmetry and periodicity properties to simplify trigonometric expressions
Prerequisites
Slides
Interactive presentations perfect for visual learners • Interactive presentation
Slide Video
Watch narrated slides play like a video lesson • Narrated slide playback
Exercises
Practice problems to build fluency and understanding • 1 exercises