What you can explore
- Control amplitude A, horizontal stretch b, phase φ (in radians or degrees), and vertical shift D in one form.
- See derived quantities—amplitude, period, frequency, phase shift, and range—update instantly beside the main equation.
- Synchronise the unit circle and function graph so θ, cosθ, sinθ, and y(θ) are always aligned.
- Copy LaTeX, share the exact state through a URL, export CSV samples, or toggle an annotated teacher mode.
Set up the trig function
Result and synced visuals
Unit circle
Projection lines show cosθ and sinθ. Special angles are marked for quick reference.
| Amplitude (sin/cos) | — |
|---|---|
| Period T | — |
| Frequency 1/T | — |
| Phase shift C = −φ/b | — |
| Vertical shift D | — |
| Range | — |
Graph of y(x)
How it’s calculated
Teacher notes
- Connect amplitude and vertical shift directly to the peaks and midline before inviting students to move θ.
- Pause animation at special angles to highlight cosθ and sinθ coordinates, then restart to show continuity.
- Use the CSV export to plot the same curve in spreadsheets or graphing utilities for comparison exercises.
Frequently asked questions
How do I represent a constant function when b = 0?
Set b to 0 and choose any φ. The explorer evaluates y = A*f(φ)+D, so the graph collapses to a horizontal line and derived results show an infinite period and zero frequency.
Can I type expressions like π/4 or √3/2?
Yes. The fields understand common math expressions including pi, sqrt(), parentheses, and basic arithmetic, so π/4 or sqrt(3)/2 are parsed safely without using eval.
متعلقہ کیلکولیٹرز
حساب کیسے کیا گیا
- Angles in degrees/radians with exact values for special angles.
- Computes (cos θ, sin θ), quadrant, and symmetries.
- Share URL preserves angle settings.