Trigonometric Functions – Sine and Cosine

Trigonometric Functions – Sine and Cosine is a ready-to-use Math teaching resource for Grades 10–12. How does mathematics describe processes that repeat themselves regularly again and again – the change between day and night, the oscillation of a spring, the height of a gondola on a Ferris wheel? This teaching series for upper secondary level leads from the foundations on the unit circle to the independent modelling of such periodic processes.

Guiding question: How do sine and cosine describe periodic processes – from the unit circle to modelling?

What's included

• 5 differentiated worksheets with required and optional tasks
• Full answer keys with expected solutions
• A 7-slide colour presentation
• A detailed, step-by-step lesson plan
• Print & digital — editable and ready to use, no prep required

Learning objectives

• Interpret sine and cosine on the unit circle as the coordinates of a point and give angles in radian measure
• Draw the graphs of sin(x) and cos(x) and describe their period, amplitude, zeros and symmetries
• Interpret the parameters a, b, c and d in f(x)=a·sin(b·(x−c))+d geometrically and determine their effect on the graph
• Read a suitable function term from given graphs of periodic functions and justify it
• Model real periodic processes such as daylight length or oscillations with sine or cosine functions and interpret them

Topics covered (5 worksheets)

• Sine and cosine on the unit circle and radian measure
• Drawing and reading the graphs of sin(x) and cos(x)
• Applying the parameters a, b, c and d
• Analysing function terms from graphs
• Modelling periodic real-world contexts

How to use it

Teach the full series in sequence or pull single worksheets as stand-alone lessons. Differentiation is built in through required and optional tasks, so you can meet a range of levels in the same class. The included lesson plan and complete answer keys make the resource ready to teach with no additional preparation.

Frequently asked questions

What grade level is Trigonometric Functions for?
It is designed for Grades 10–12 (Math), and the differentiated tasks let you adapt it up or down a level.

What file formats are included?
You receive editable Microsoft Word worksheets and answer keys, an editable PowerPoint presentation, and a Word lesson plan — all print-ready and suitable for digital classrooms.

Is it ready to use without preparation?
Yes. Everything is classroom-ready: print the worksheets or share them digitally, present the slides, and use the answer keys and lesson plan as-is.

Created with support from ChatGPT (OpenAI) and Claude (Anthropic).