The Discovery of Trigonometric Ratios

Updated: 6/8/2020

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- Trigonometry in the modern sense began with the Greeks. Hipparchus was the first to construct a table of values for a trigonometric function.
- The Discovery of Trigonometric Ratios
- Today we're going to learn about the discovery of Trig Ratios.
- Opposite
- He considered every triangle as being inscribed in a circle, so that each side becomes a chord (a straight line that connects two points on a curve or surface). To compute the various parts of the triangle, one has to find the length of each chord as a function of the central angle that subtends it—or, equivalently, the length of a chord as a function of the corresponding arc width.
- Adjacent
- Hypothenuse
- sin = Opp/Hypcos = Adj/Hyptan = Opp/Adj
- Adjacent
- SineCosine Tangent
- SOHCAHTOA
- In Hipparchus’s time these formulas were expressed in purely geometric terms as relations between the various chords and the angles (arcs) that subtend them; the modern symbols for the trigonometric functions were not introduced until the 17th century.
- This became the chief task of trigonometry for the next several centuries. As an astronomer, Hipparchus was mainly interested in spherical triangles, such as the imaginary triangle formed by three stars on the celestial sphere, but he was also familiar with the basic formulas of plane trigonometry.
- SineCosineTangent
- I'm going to be showing you an example of how to apply Trig Ratios using a diagram
- Applying Trigonometric RatiosExample 1
- 5
- A
- a
- 19
- B
- Find the measure of angle A.
- THINK...Sin, Cos, TanSOH, CAH, TOA
- 5
- A
- Hence, by applying both trig ratios and inverse trig ratios, you can find the measure of a missing angle in a triangle.
- a
- 19
- B
- cosA = 5/19A= cos^-1 (5/19)A= 74.74 degrees