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Introduction to Trigonometry

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A ladder rests against a wall. One angle. Three sides. Six ratios.

One angle, three sides, three ratios.

Chapter 8 is Introduction to Trigonometry. It names the ratios of a right triangle. It proves one identity about them. An identity is an equation true for every acute angle.

What this track covers

  • Naming the sides — opposite, adjacent and hypotenuse for one angle.
  • Three ratios and their flips — sin, cos, tan and cosec, sec, cot. A flip is 1 divided by the ratio.
  • The angle owns the ratio — same angle, same ratio, any size.
  • The exact values — for 0°, 30°, 45°, 60° and 90°. Exact means not rounded.
  • One identity — sin²A + cos²A = 1, and two more that follow.

Quick catch-up

  • A ratio is one number divided by another.
  • The hypotenuse is the side across from the right angle.
  • In a right triangle, a² + b² = c². Here c is the hypotenuse.
  • A right angle is exactly 90°.
  • An acute angle is smaller than 90°.
  • An equilateral triangle has three equal sides and three 60° angles.

Open the chapter. Read every exercise as a triangle to name.

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This track

  1. 0 Start here
  2. 1 Naming the ratios
  3. 2 The angle owns the ratios
  4. 3 The flipped ratios
  5. 4 The flat end and the upright end
  6. 5 Forty-five degrees, folded from a square
  7. 6 Checkpoint: ratios, flips and one fold
  8. 7 Thirty and sixty, cut from an equilateral
  9. 8 Quotients of quotients
  10. 9 Squared, then added
  11. 10 Checkpoint: values, relations and the identity
  12. 11 What the identity settles
  13. 12 The big picture
  14. 13 Track quiz

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