Lesson Plan

• Describe the effect of the parameters a, b and c on the shape and position of sine, cosine and tangent graphs.
• Calculate amplitude, period and vertical shift for transformed sine and cosine functions and determine asymptote locations for tangent functions.
• Sketch accurate graphs of y = a sin(bx)+c, y = a cos(bx)+c and y = a tan(bx)+c over a specified domain.
• Identify and label all vertical asymptotes of a tangent graph within a given interval.
• Apply the sketching procedure to solve exam‑style practice questions.

• Projector and screen
• Graph paper and rulers
• Scientific calculators
• Worksheet with practice questions
• Printed summary of transformation rules
• Whiteboard and markers

Begin with a brief recall of the basic shapes of sine, cosine and tangent graphs. Highlight that today’s focus is on how the parameters a, b and c transform these graphs and how to locate asymptotes for tangent functions. State that students will demonstrate mastery by correctly sketching three transformed functions on their worksheets.

1. Do‑Now (5′): Quick quiz on amplitude and period of untransformed sine/cosine; teacher reviews answers.
2. Mini‑lecture (10′): Review the roles of a, b and c, derive period formulas, and introduce tangent asymptote formula; use projector examples.
3. Guided sketching (15′): Whole‑class step‑by‑step sketch of y = 2 sin(3x)‑1, modelling each transformation stage.
4. Paired activity (15′): Students choose a cosine and a tangent function from cards, sketch them, label key points and asymptotes; teacher circulates for feedback.
5. Check for understanding (5′): Exit ticket – write the period formula for a given b and list asymptote positions for a tangent function.
6. Summary & homework (5′): Recap the five‑step procedure, assign the worksheet with three additional graphing problems for practice.

Summarise the transformation steps and emphasise the distinct period and asymptote behaviour of tangent functions. Collect exit tickets to gauge immediate understanding and remind students to complete the assigned practice worksheet for reinforcement.