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- Trigonometry in the modern sense began with the#160;Greeks.#160;Hipparchus#160;was the first to construct a table of values for a#160;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#160;line#160;that connects two points on a curve or#160;surface).#160;#160;To compute the various parts of the triangle, one has to find the length of each chord as a#160;function#160;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#160; #160; #160;= Opp/Hypcos#160; #160; #160;= Adj/Hyptan#160; #160; #160;= Opp/Adj
- Adjacent
- SineCosine#160;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#160;stars#160;on the#160;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#160;to apply Trig Ratios using a diagram
- Applying Trigonometric RatiosExample 1
- THINK...Sin, Cos, TanSOH, CAH, TOA
- Find the measure of angle A.
- 5
- A
- a
- 19
- B
- 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
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