surface example

3D Product Sine Cosine Graph

A checkerboard-like wave surface.

z = sin(x) * cos(y)

Quick facts

  • Formula: z = sin(x) * cos(y)
  • Category: surface
  • Tags: surface, calculus, z=f(x,y)

What this graph represents

Multiplying the waves makes positive and negative regions alternate.

Where it appears in calculus

Use it to connect sign patterns to surface height.

How to use this graph

  1. Rotate the surface by dragging with your mouse or finger
  2. Use the Embed button to copy an <iframe> for your LMS or lesson page
  3. Click PNG to export a classroom-ready image
  4. Click Formula or LaTeX to copy the equation for your notes

Embed this graph

Use the Embed button in the calculator to copy a ready iframe for blogs, LMS pages, and lesson notes.

Open embed page

Teacher prompt

Question: Why do some hills become valleys?

Answer: The product changes sign when either sine or cosine changes sign.

Related graphs

Explore more surface examples and compare shapes, slices, and contour behavior.

Absolute Value Pyramid

z = abs(x) + abs(y)

A four-sided pyramid made from absolute values.

Cubic Surface

z = x^3 - y

A cubic sheet tilted by the y term.

Log Bowl

z = log(1 + x^2 + y^2)

A bowl that rises slowly as it moves outward.

Square Root Dome

z = sqrt(max(0, 16 - x^2 - y^2))

The upper half of a sphere-like dome.

Hyperbolic Valley

z = x*y

A saddle-like surface formed by multiplying x and y.

Cosine Hills

z = cos(x) + cos(y)

A regular field of smooth hills and basins.

Explore more tools

Use these free browser tools to extend your graphing workflow.

3D Surface Plotter

Plot z=f(x,y), rotate, and export

Embed Builder

Create ready-to-use iframe embeds

Worksheet Export

Export graph images for classroom worksheets

How to Graph z=f(x,y)

Step-by-step guide for beginners