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Introduction to Trigonometry Part 1

Introduction to Trigonometry Part 1. If you know 2 sides of a right triangle…. You can find the third side. A ² + B² = C² B² = C² - A² A² = C² - B². b. C. A. a. B. If you know 2 angles…. You can find the missing angle. ma = 180 - (90 + mb) mb = 180 - (90 + ma). b. C. A.

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Introduction to Trigonometry Part 1

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  1. Introduction to TrigonometryPart 1

  2. If you know 2 sides of a right triangle… • You can find the third side. • A² + B² = C² • B² = C² - A² • A² = C² - B² b C A a B

  3. If you know 2 angles… • You can find the missing angle. • ma = 180 - (90 + mb) • mb = 180 - (90 + ma) b C A a B

  4. What if you know one side & one angle and you want to find the missing sides? • Now you need to use trigonometry! • First we have to learn some vocabulary.

  5. Some vocabulary: • The hypotenuse (hyp) is the longest side of the triangle – it is always across from the right angle • The opposite (opp) is the side directly across from the reference angle • The adjacent (adj) is the side next to the reference angle

  6. A picture always helps… • Let b be your reference angle • A is the adjacent side (next to the angle) b C A • B is the opposite side (across from the angle) B b Next • C is always the hypotenuse hyp Longest adj opp Across

  7. But if we switch angles… • Now let a be your reference angle • A is the opposite (across from the angle) C A a • B is the adjacent (next to the angle) B Across • C is always the hypotenuse hyp Longest opp a adj Next

  8. Let’s practice… label each side relative to the reference angle.

  9. Trigonometry uses ratios of the sides • There are three sets of ratios for any triangle • sin…short for sine • cos…short for cosine • tan…short for tangent

  10. So what are the formulas? Tan is Opposite over Adjacent Sin is Opposite over Hypotenuse Cos is Adjacent over Hypotenuse SOH CAH TOA

  11. If you need more help in memorizing… • Soh-Cah-Toa • Some old horse Caught another horse Taking oats away. • Some old horse Caught another horse Trotting on asphalt.

  12. Calculating a side if you know the angle • you know a side (adj) and an angle (25°) • we want to know the opposite side b C A 25° B = 6

  13. And one sin example • find the length of side A • We have the angle and the hyp, and we need the opp b C = 20 A 25° B

  14. What are the steps for doing one of these questions? • Label the sides • Choose SOH, CAH, or TOA • Solve the equation for the unknown value • Does the answer make sense?

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