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Thought-Process to Discover Knowledge
Welcome to the only place where the trigonometric values on unit circle is properly connected to the trigonometric ratios of right-triangles.
• The trigonometric ratios of right-triangles are defined as -- "The right-triangles having a given angle are similar. The ratio of sides for those right-triangles is a known constant".
• The trigonometric values on unit-circle are defined as -- "The representative similar triangle is taken in unit-circle with hypotenuse `1`. The trigonometric ratios become into the horizontal and vertical projections.".
The thought-process in the above is revolutionary and aweinspiring.
The trigonometric values for all quadrants and for compound angles are also covered.
(click for the list of lessons in this topic)
Trigonometric Identities for compound angles
In this page, expressing trigonometric values for sum or difference of two angles, in terms of the trigonometric functions of the two angles is explained.
This provides very simple proofs for trigonometric identities of compound angles, `sin(A+B)`, `cos(A+B)` etc.