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3D Trigonometry Introduction
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3D Trigonometry Introduction
📐 Part 1: 3D Coordinate System Basics
1. The three axes in a 3D coordinate system are perpendicular to each other. What are they called?
X-axis, Y-axis, Z-axis
Length, Width, Height
Horizontal, Vertical, Diagonal
A-axis, B-axis, C-axis
2. A point in 3D space is represented as (x, y, z). Which coordinate represents the vertical position?
x-coordinate
y-coordinate
z-coordinate
All coordinates equally
3. How many octants (regions) are created when the three coordinate planes divide 3D space?
4
6
8
12
4. Plot the following points on the 3D coordinate system below: A(2, 1, 3), B(-1, 2, 0), C(0, -2, 1)
📏 Part 2: Lines, Planes and Angles in 3D
5. Which of the following best describes a plane in 3D space?
A curved surface extending infinitely
A flat 2D surface extending infinitely in 3D space
A line with thickness
A collection of separate points
6. Select all the types of angles we can measure in 3D space:
Angle between two intersecting lines
Angle between a line and a plane
Angle between two planes
Angle between two parallel lines
7. The line joining the origin (0,0,0) to the point (1,1,0) makes what angle with the x-axis?
Angle = _________ degrees
8. Explain in your own words how measuring angles in 3D space differs from measuring angles in 2D space.
🎯 Part 3: Application and Reflection
9. A rectangular room has dimensions 4m × 3m × 2.5m (length × width × height). If you place the origin at one corner on the floor, write the coordinates of all 8 corners of the room.
10. Real-world application: Name two situations where understanding 3D trigonometry would be useful.
Situation 1: _________________________________________________
Situation 2: _________________________________________________
11. Reflection: What is one concept from today's lesson that you found challenging and would like to explore further?
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