Comparing Khan academy and nubtrek trigonometry

One of the key driver of nubtrek.com is to change the content available for students. In books and websites, the content is broadly presented as “matter-of-fact” which students learn as-is. Instead, nubtrek provides a “thought-process” which enable students to figure out. This “comparison” series will bring out and juxtapose such content.

matter-of-fact knowledge

Khan academy trigonometry outline is to introduce and explain the following one by one.

Reference: Khan Academy

• right-triangles
• hypotenuse
• opposite side
• adjacent side

This is matter-of-fact knowledge… information is provided as matter-of-fact and students are expected to learn as-is.

thought-process in nubtrek

nubtrek explains the same in a thought-process

reference : nubtrek

• triangles have 3 independent parameters. eg: Given Angle-Side-Angle, the other sides and the angle can be computed.
• right triangles have 2 independent parameters. eg: Given one angle and one side, the other sides and the angle can be computed.
• class of similar right triangles have 1 independent parameter. eg: Given one angle, the ratio of sides are fixed and the other angle can be computed
• trigonometric ratios capture the ratio-of-sides given an angle of class of similar right triangles.
• thus the sides with reference to the given angle are named as hypotenuse, opposite side, and adjacent side.
• the constants for the given angle θ are named as sin, cos, tan etc.
• This knowledge helps you with finding other parameters of right-triangles once an angle and a side is specified.
• eg: Given angle as 45 degree, and one arm of right angle is 3, it is immediately computed that other arm of right angle is 3 and the hypotenuse is 3sqrt(2).

The thought process is to

• start with independent parameters in triangles,
• develop knowledge to define the relationship of independent parameters to other derived parameters and
• explain how to use this knowledge to analyse the other derived parameters using the given independent parameters.

Students are given with the right thought-process to learn the knowledge.

Thanks for reading.