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Thought-Process to Discover Knowledge

Welcome to nubtrek.

Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

Read in the blogs more about the unique learning experience at nubtrek.continue
9th-10th Foundation


Welcome to the only place where the essence of trigonometry is explained.

 •  a right-triangle is specified by 2 independent parameters.

 •  That means, if an angle and the length of a side is given, then one should be able to calculate the length of the other two sides.

 •  What property one can use to calculate the above? For a given angle, the ratio of sides is a constant.

Thus, the ratio of sides comes into existence as `sin`, `cos`, `tan` etc. The thought-process is revolutionary and aweinspiring.

Beyond the definitions of trigonometric ratios, the following are covered.

 •  trigonometric ratios for standard angles

 •  trigonometric identities based on Pythagoras Theorem
(click for the list of lessons in this topic)

Trigonometric Ratios for Standard Angles

Learn something made astoundingly easy: Trigonometric ratios for standard angles, derived from

 •  equilateral triangles `30^@` and `60^@`,

 •  isosceles right-triangles `45^@`, and

 •  a triangle with one-side zero `90^@` and `0^@`.

Once the basis of standard angles is understood as the different triangles given above, the values of trigonometric ratios are very very easy to quickly calculate. No need to blindly memorize.

(click for the list of pages in the lesson)