What stays fixed

A rotation about the x-axis leaves every xx coordinate unchanged. Only the yy and zz components are remixed.

That is why the first row and first column keep the identity pattern while the lower-right 2×2 block behaves like a usual planar rotation.

Use the preview to sanity-check the direction before copying the matrix into graphics, robotics, or class notes.

Quick reminders

  • Positive angles follow the right-hand rule about the x-axis.
  • The rotating part is the 2×2 block with coshetacos heta and sinhetasin heta.
  • Radians are useful when the angle already comes from calculus or a simulation pipeline.

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