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88btrigintro 090522115837-phpapp01

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Transcript of "88btrigintro 090522115837-phpapp01"

  1. 1. Sine/Cosine/Tangent Focus: Find out who is sohacahtoa and why is the spelling of his name so important?
  2. 2. sohcahtoa • SOHCAHTOA was the chief of the Trigonometric Tribe. He was a very wise man and people would go to him to solve their most pressing problems. Legend has it that he is the grandson of Sacajewea, for whom a famous park was erected in SW Washington state in time for Lewis and Clark to have a bath.
  3. 3. sohcahtoa • SOHCAHTOA, a contemporary of Pythagorus, worked on finding ways to solve lengths and distances on right triangles. • SOHCAHTOA is a famous dead mathematician, but his name lives on in legendary brilliance, he is still alive and working with roots. • Spell his name correctly and you will certain pass into the tribe of Trigonometry’s lore.
  4. 4. Right Triangles’ Sides • Hypotenuse • Adjacent side • Opposite side • The adjacent and opposite sides are relative terms, compared to the location of the angle in question. • The hypotenuse is always across from the right angle in a triangle.
  5. 5. Where they are found. 25°
  6. 6. Where the hypotenuse is found. hypotenuse 25°
  7. 7. Where the adjacent and opposite sides are found. hypotenuse 25° opposite Adjacent means next to or attached. This will be shown on the next slide.
  8. 8. Where the adjacent and opposite sides are found. hypotenuse 25° Adjacent side to the 25° angle. Adjacent means next to or attached. The next slide will show the relationships from the remaining angle. Opposite the 25° angle.
  9. 9. Where the adjacent and opposite sides are found relative to the third angle.. hypotenuse 65° Adjacent side Adjacent means next to or attached. The hypotenuse is still (always) across from the right angle. Opposite the 65 degree angle.
  10. 10. Ratios • Sine ratio: – Opposite over hypotenuse • Cosine ratio: – Adjacent over hypotenuse • Tangent ratio: – Opposite over Adjacent 9 12 15 Trigonometry is based on the following relationships. x°
  11. 11. Ratios • Sine ratio: – Opposite over hypotenuse 9 12 15 x° 9 15
  12. 12. Ratios • Sine ratio: – Opposite over hypotenuse • Cosine ratio: – Adjacent over hypotenuse 9 12 9 12 15 x° 12 15
  13. 13. Ratios • Sine ratio: – Opposite over hypotenuse • Cosine ratio: – Adjacent over hypotenuse • Tangent ratio: – Opposite over Adjacent 9 15 9 12 15 x° 9 12 12 15
  14. 14. Ratios • Sine ratio: – Opposite over hypotenuse • Cosine ratio: – Adjacent over hypotenuse • Tangent ratio: – Opposite over Adjacent 9 12 15 Trigonometry charts are usually found at the back of math textbooks. Is there one in your book on page 668? x° 9 15 9 12 12 15 We can use these fractions as division statements and compare the resulting answers to determine the angle’s measurement.
  15. 15. What is the missing angle measurement? .8000= 9 15 = 9 12 12 15 .6000= .7500=
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