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Introduction to Trigonometry

Finding sides from angles. Introduction to Trigonometry. Trigonometry is…. A branch of geometry used first by the Egyptians and Babylonians (Iraq) Used extensively is astronomy and building Based on ratios between angles in RIGHT Triangles. Ratio Name sine cosine tangent cotangent

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Introduction to Trigonometry

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  1. Finding sides from angles Introduction to Trigonometry

  2. Trigonometry is… • A branch of geometry used first by the Egyptians and Babylonians (Iraq) • Used extensively is astronomy and building • Based on ratios between angles in RIGHT Triangles

  3. Ratio Name sine cosine tangent cotangent secant cosecant Abbreviation sin cos tan cot sec csc The ratios have names and abbreviations…

  4. The Trigonometric (trig) ratios: FUNCTION INVERSE FUNCTION

  5. Also true are…

  6. SOH CAH TOA There was a beautiful Native American Princess named Soh Cah Toa. She taught the early American settlers to remember their basic trig functions by remembering her name. Her first name “Soh” stands for “sin = opposite/hypotenuse”. Her middle name “Cah” stands for “cos = adjacent/hypotenuse”. Her last name “Toa” stands for “tan = opposite/adjacent”. The early settlers were very thankful to Soa Cah Toa. They were able to build their homes and remember their trigonometry forever. And they always wrote down Soa Cah Toa’s name before beginning any of their work.

  7. In the ratios: • x is an angle (not the 90 degree angle) • “adjacent”, “opposite” and “hypotenuse” are all side lengths, not angles • “Adjacent” is the side next to the known angle • “Opposite” is the side across from the known angle

  8. Greek Theta Is the Greek letter Theta It is often used in place of “x” when naming angles.

  9. Here we name one angle Theta

  10. !IMPORTANT! To solve trig functions in the calculator, make sure to set your MODE to DEGREES • Directions: Press MODE, arrow down to Radian Arrow over to Degrees Press ENTER

  11. Example:Find the missing side lengths.

  12. We have one angle (30°) and the hypotenuse. • Which ratios can we use to find the other sides?

  13. You try: • Find the hypotenuse length and the values of the 5 other trig functions for: Hint: use a2 + b2 = c2 to find the hypotenuse!

  14. Did you get…

  15. Why is this useful? • Imagine being an Ancient Egyptian. They had no calculators, no computers. They could use one angle and a pyramid’s side length to find the other side lengths.

  16. Classwork: • Page 764: #2 – 6 • Page 765: #13 – 21 • Just write the ratios • Don’t try to • Solve for angles yet

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