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More Ratios….and more Latin..

More Ratios….and more Latin. Given a triangle, how many different ratios can we make?. There are 2 more ratios we need to examine…. The next ratio, will be…. O. hypotenuse. opposite. “theta”. adjacent. This ratio was first studied by Hipparchus (Greek), in 140 BC.

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More Ratios….and more Latin..

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  1. More Ratios….and more Latin..

  2. Given a triangle, how many different ratios can we make?... There are 2 more ratios we need to examine…

  3. The next ratio, will be… O hypotenuse opposite “theta” adjacent

  4. This ratio was first studied by Hipparchus (Greek), in 140 BC.

  5. Aryabhata (Hindu) continued his work. For this ratio OPP/HYP, the word “Jya” was used

  6. Brahmagupta, in 628, continued studying the same relationship and“Jya” became “Jiba” later, “Jiba became Jaib”whichmeans “fold” in Arabic

  7. European Mathmeticians eventually translated “jaib” into latin: SINUS

  8. Later compressed to the singular “SINE” by Edmund Gunter in 1624 Compressed again by calculator manufactorers into.. SIN

  9. 1 A X 12 12 X SIN32O = 12 FIND A: 1 12 X SIN32O = A A = 6.4 m 12 m A 32O

  10. Given a right triangle, the 2 remaining angles must total 90O. A = 10O, then B = 80O A = 30O, then B = 60O A A “compliments” B C B

  11. The last ratio will be… The adjacent/hyp ratio compliments the opposite/hyp ratio (called SIN)….therefore O hypotenuse opposite “theta” adjacent

  12. Therefore, ADJ/HYP is called “Complimentary Sinus” COSINE COS

  13. The 3 Primary Trig Ratios SINO = opp O hyp COSO = adj hyp hyp opp TANO = opp adj adj

  14. soh cah toa 1 A X 17 FIND A: 17 X COS25O = 17 1 A = 17 X cos25O 17m A = 15.4 m 25O A

  15. soh cah toa 1 A X 10 FIND A: 10 X SIN37O = 10 1 A = 10 X SIN37O 10 m A = 6.02 m A 37O

  16. soh cah toa 1 A X 10 FIND A: 10 X TAN63O = 10 1 A = 10 X TAN63O 63O A = 19.6 m 10 m A

  17. O O O O Now we have 3 working ratios for every possible right sided triangle at our fingertips….

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