Math9-12+
Sine and Cosine Transformations Guided Notes
By Gwen S.
A guided-notes packet for high school trigonometry that walks students through identifying amplitude, period, phase shift, vertical shift, and range from sinusoidal equations. It builds skills in reading function transformations and connecting equation constants to graph features, with fill-in tables to scaffold the note-taking.
Customize for your classroom
Teacher Guide & Tips
- Use as a 30 to 45 minute mini-lesson or warm-up before students graph sine and cosine functions independently, pairing it with a graphing calculator or Desmos.
- Discussion question: How does changing the value of B affect the period, and why does the formula use the absolute value of B?
- Scaffold for struggling readers: Start by graphing y = sin(x) and y = 2sin(x) side by side so students see amplitude as vertical stretch before tackling B and C.
- Extension for advanced students: Have them write y = A sin(B(x - C)) + D for a graph they sketch from scratch, then justify why the phase shift sign is opposite to the direction of the shift.
- Estimated time: about 20 minutes to complete the notes table, plus additional practice time for graphing.
Math9-12+
Sine and Cosine Transformations Guided Notes
By Gwen S.
A guided-notes packet for high school trigonometry that walks students through identifying amplitude, period, phase shift, vertical shift, and range from sinusoidal equations. It builds skills in reading function transformations and connecting equation constants to graph features, with fill-in tables to scaffold the note-taking.
Customize for your classroom
Teacher Guide & Tips
- Use as a 30 to 45 minute mini-lesson or warm-up before students graph sine and cosine functions independently, pairing it with a graphing calculator or Desmos.
- Discussion question: How does changing the value of B affect the period, and why does the formula use the absolute value of B?
- Scaffold for struggling readers: Start by graphing y = sin(x) and y = 2sin(x) side by side so students see amplitude as vertical stretch before tackling B and C.
- Extension for advanced students: Have them write y = A sin(B(x - C)) + D for a graph they sketch from scratch, then justify why the phase shift sign is opposite to the direction of the shift.
- Estimated time: about 20 minutes to complete the notes table, plus additional practice time for graphing.