3D Trigonometry

• 3D trigonometry is a branch of mathematics that uses principles from Right-Angle Trigonometry and Pythagoras’ Theorem to solve problems involving three-dimensional shapes.

• It’s pivotal to know the basic 2D trigonometric ratios: sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, and tan θ = opposite/adjacent. These principles are equally applicable in 3D trigonometry.

• In 3D problems, one must first identify the right-angled triangle involved.

• Another necessary element to understand is the right-angled triangle’s sides: the opposite (perpendicular to the angle), the adjacent (next to the angle and the right angle), and the hypotenuse (the longest side opposite the right angle).

• The three-dimensional version of Pythagoras’ Theorem can be used to find the length of a line segment in a three-dimensional space. If the segment has endpoints with coordinates (x1, y1, z1) and (x2, y2, z2), then the length of the segment is √[(x2 − x1)^2 + (y2 − y1)^2 + (z2 − z1)^2].

• 3D Trigonometry is commonly used to solve real life problems such as finding the angles between intersecting lines or planes, the height of a tall object from a certain distance and angle of elevation, or establishing the shortest distance between two points in 3D space.

• It is important to practise 3D trigonometry problems. Visualizing the problem or using models can help with understanding.

• Always check the results. If the angles do not add up to 180 degrees or if the sides do not satisfy Pythagoras’ theorem in a right angled triangle, then the answer is likely incorrect.

• Past problem sets filled with 3D Trigonometry-related questions will often help with grasping the principles better. Do ensure regular practise to solidify your understanding and improve speed during assessments.

• 3D Trigonometry is often tested in conjunction with other topics, such as geometry, algebra and problem-solving, so a solid grasp of these areas can also be beneficial.