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Trigonometry: SOH-CAH-TOA & Unit Circle

72 cards · 🇺🇸 English

Right-triangle trig ratios and the unit circle.

trigonometryunit-circlesoh-cah-toa

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SOH-CAH-TOA

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  1. 1SOH-CAH-TOA
    Sine = Opposite ÷ Hypotenuse, Cosine = Adjacent ÷ Hypotenuse, Tangent = Opposite ÷ Adjacent
  2. 2Sine (sin) of an angle in a right triangle
    The ratio of the side opposite the angle to the hypotenuse
  3. 3Cosine (cos) of an angle in a right triangle
    The ratio of the adjacent leg to the hypotenuse
  4. 4Tangent (tan) of an angle in a right triangle
    The ratio of the opposite leg to the adjacent leg
  5. 5Cosecant (csc) function
    The reciprocal of sine: csc(θ) = 1/sin(θ)
  6. 6Secant (sec) function
    The reciprocal of cosine: sec(θ) = 1/cos(θ)
  7. 7Cotangent (cot) function
    The reciprocal of tangent: cot(θ) = 1/tan(θ)
  8. 8Unit circle
    The circle of radius 1 centered at the origin in the coordinate plane
  9. 9On the unit circle, what do the coordinates (x,y) represent for an angle θ?
    x = cos(θ) and y = sin(θ)
  10. 10Sin(0°)
    0
  11. 11Cos(0°)
    1
  12. 12Tan(0°)
    0
  13. 13Sin(30°)
    1/2
  14. 14Cos(30°)
    √3/2
  15. 15Tan(30°)
    1/√3 or √3/3
  16. 16Sin(45°)
    √2/2 or 1/√2
  17. 17Cos(45°)
    √2/2 or 1/√2
  18. 18Tan(45°)
    1
  19. 19Sin(60°)
    √3/2
  20. 20Cos(60°)
    1/2
  21. 21Tan(60°)
    √3
  22. 22Sin(90°)
    1
  23. 23Cos(90°)
    0
  24. 24Tan(90°)
    Undefined
  25. 25Fundamental Pythagorean identity
    sin²(θ) + cos²(θ) = 1
  26. 26Pythagorean identity for tangent and secant
    1 + tan²(θ) = sec²(θ)
  27. 27Pythagorean identity for cotangent and cosecant
    1 + cot²(θ) = csc²(θ)
  28. 28Period of the sine function
    2π radians (or 360°)
  29. 29Period of the cosine function
    2π radians (or 360°)
  30. 30Period of the tangent function
    π radians (or 180°)

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