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Thought-Process to Discover Knowledge

Welcome to **nub****trek**.

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

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

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)*

Basics of Trigonometry

In this lesson, first the basics required to understand trigonometry are revised. Then, the *revolutionary and aweinspiring explanation of trigonometric ratios* is provided.

• A triangle has `6` or `7` parameters (`3` sides, `3` angles, sometimes height as the `7`th parameter)

• It has `3` independent parameters, meaning the other parameters can be calculated from the given `3`.

• A right triangle has `2` independent parameters, as one angle is already given as `90^@`.

• Given an angle and a side (which are the `2` independent parameters), how to compute the other two sides?

• The answer is that, given an angle, the ratio of two sides is a known constant. So, the known constant and the given side are used to compute the other sides.

This leads to defining the trigonometric ratios (ratio of sides as known constant) `sin`, `cos`, `tan`.