Trig Graph with Period, Amplitude and Phase Labelled
A sine, cosine or tangent graph with amplitude, period, phase shift and key points marked.
Makes images - needs an image AI · Best tool: ChatGPT or Gemini (image)
✅ How to use this effectively
- 1. Open an image-capable AI chat.
- 2. Paste the prompt below.
- 3. Type your trig function in the INPUT line.
- 4. Send and check the period and amplitude.
- 5. Download the graph.
🔧 If it is not right, reply with this: If the period looks wrong, reply: "Recompute the period as 2 pi divided by the coefficient of x, re-mark the axis, and redraw."
THE PROMPT
ROLE: Act as a trigonometry teacher who graphs trig functions and labels every key feature. CONTEXT: I teach [CLASS/GRADE] under [BOARD or EXAM e.g. CBSE / ICSE / JEE]. The graph must show amplitude, period, phase shift, vertical shift and key points so students see how the parameters change the curve. YOUR TASK: 1. Plot the trig function over at least one full period (two is better) on labelled axes, with the x-axis marked in terms of pi (pi/2, pi, 3pi/2, 2pi) and a light grid. 2. Label the amplitude with a vertical measure, the period with a horizontal measure, and any phase shift and vertical shift. 3. Mark the maximum points, minimum points, and points where the curve crosses its midline. 4. Draw the midline as a dashed horizontal line, and asymptotes as dashed verticals for tangent. 5. Write the function's equation in a corner. INPUT: Here is the function: [PASTE IT HERE, e.g. y = 2 sin(x), y = cos(2x), y = sin(x - pi/4) + 1, y = tan(x)]. HOW TO WORK IT OUT: First read off the parameters and compute on the side: amplitude = |A|, period = 2 pi / |B| (or pi / |B| for tangent), phase shift from the horizontal translation, and vertical shift. Show this working. VERIFY two ways: substitute one key x-value (such as a maximum point) back into the function and confirm the y-value, and confirm the distance between two consecutive maxima equals the computed period. Never mislabel period as amplitude; never invent a shift that is not in the equation. OUTPUT FORMAT: 1. PARAMETERS: amplitude, period, phase shift, vertical shift with the working. 2. THE GRAPH: one clean labelled image with axis in multiples of pi, marked max/min/midline crossings, midline dashed, asymptotes if tangent, and the equation shown. 3. CHECK: one line giving the substitution check and the maxima-spacing check. RULES: x-axis in multiples of pi. Amplitude and period clearly distinguished and measured. Midline and asymptotes dashed. Plain white background. SIGNATURE: Sign the bottom-right of every page with an elegant handwritten signature "[YOUR NAME]" with a small underline flourish.