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2. List of trigonometric identities - Wikipedia

   en.wikipedia.org/wiki/List_of_trigonometric...

   The reciprocal identities arise as ratios of sides in the triangles where this unit line is no longer the hypotenuse. The triangle shaded blue illustrates the identity 1 + cot 2 ⁡ θ = csc 2 ⁡ θ {\displaystyle 1+\cot ^{2}\theta =\csc ^{2}\theta } , and the red triangle shows that tan 2 ⁡ θ + 1 = sec 2 ⁡ θ {\displaystyle \tan ^{2 ...

3. Law of reciprocal proportions - Wikipedia

   en.wikipedia.org/wiki/Law_of_reciprocal_proportions

   This ratio of 1.19 obeys the law because it is a simple fraction (1/3) of 3.58. (This is because it corresponds to the formula ICl 3, which is one known compound of iodine and chlorine.) Similarly, hydrogen, carbon, and oxygen follow the law of reciprocal proportions. The acceptance of the law allowed tables of element equivalent weights to be ...

4. Exact trigonometric values - Wikipedia

   en.wikipedia.org/wiki/Exact_trigonometric_values

   In the table below, the label "Undefined" represents a ratio : If the codomain of the trigonometric functions is taken to be the real numbers these entries are undefined , whereas if the codomain is taken to be the projectively extended real numbers , these entries take the value ∞ {\displaystyle \infty } (see division by zero ).

5. Ratio - Wikipedia

   en.wikipedia.org/wiki/Ratio

   The ratio of width to height of standard-definition television. In mathematics, a ratio (/ ˈ r eɪ ʃ (i) oʊ /) shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3).

6. Conversion of units - Wikipedia

   en.wikipedia.org/wiki/Conversion_of_units

   Thus, to convert from units of Fahrenheit to units of Celsius, one subtracts 32 °F (the offset from the point of reference), divides by 9 °F and multiplies by 5 °C (scales by the ratio of units), and adds 0 °C (the offset from the point of reference).

7. Special right triangle - Wikipedia

   en.wikipedia.org/wiki/Special_right_triangle

   A "side-based" right triangle is one in which the lengths of the sides form ratios of whole numbers, such as 3 : 4 : 5, or of other special numbers such as the golden ratio. Knowing the relationships of the angles or ratios of sides of these special right triangles allows one to quickly calculate various lengths in geometric problems without ...