Which of the following is one of the basic ways to represent three-dimensional space in trigonometry?

• A. Using a two-dimensional plane with axes $x$ and $y$ only
• B. Using polar coordinates with one angle and one radius
• C. Using only a single axis labeled $x$
• D. Using three mutually perpendicular axes labeled $x$, $y$, and $z$

Answer: (D)

Verified step by step guidance

1. Understand that representing three-dimensional space in trigonometry requires a coordinate system that can describe any point in 3D space uniquely.
2. Recall that a two-dimensional plane with axes \(x\) and \(y\) can only represent points in 2D, so it is insufficient for 3D representation.
3. Recognize that polar coordinates with one angle and one radius describe points in a plane (2D) and cannot fully represent 3D space.
4. Note that using only a single axis labeled \(x\) represents a one-dimensional line, which is also insufficient for 3D space.
5. Identify that the standard and basic way to represent three-dimensional space is by using three mutually perpendicular axes labeled \(x\), \(y\), and \(z\), forming a 3D coordinate system.