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8 8b Trig Intro

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Sine Cosine Tangent

Sine Cosine Tangent

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  • 1. Sine/Cosine/Tangent Focus: Find out who is sohacahtoa and why is the spelling of his name so important?
  • 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. 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. 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. Where they are found. 25°
  • 6. Where the hypotenuse is found. hypotenuse 25°
  • 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. 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. 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. 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. Ratios
    • Sine ratio:
      • Opposite over hypotenuse
    9 12 15 x °
  • 12. Ratios
    • Sine ratio:
      • Opposite over hypotenuse
    • Cosine ratio:
      • Adjacent over hypotenuse
    9 12 15 x °
  • 13. Ratios
    • Sine ratio:
      • Opposite over hypotenuse
    • Cosine ratio:
      • Adjacent over hypotenuse
    • Tangent ratio:
      • Opposite over Adjacent
    9 12 15 x °
  • 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 ° We can use these fractions as division statements and compare the resulting answers to determine the angle’s measurement.
  • 15. What is the missing angle measurement?

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