surface example

3D Cosine Hills Graph

A regular field of smooth hills and basins.

z = cos(x) + cos(y)

Quick facts

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

What this graph represents

Each axis contributes one cosine wave.

Where it appears in calculus

Good for teaching periodic extrema.

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: Where do the tallest peaks appear?

Answer: They appear where both cosine terms are 1.

Related graphs

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

Egg Crate Surface

z = sin(x) * sin(y)

A repeating grid of peaks and pits.

Radial Decay

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

A smooth mound that decays toward zero.

Mexican Hat Surface

z = (1 - x^2 - y^2) * exp(-(x^2 + y^2) / 2)

A central peak surrounded by a circular valley.

Ridge Surface

z = exp(-x^2)

A ridge that is constant in the y direction.

Valley Surface

z = y^2 - 2*x

A parabolic valley tilted along the x-axis.

Spiral Height Surface

z = atan(y / (x + 0.001))

A wrapped height field based on angle.

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