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Edited by Ethan Reese, Teresa

This page is a step by step process to deriving the cosine difference formula, hopefully this can help you understand the process behind deriving the cosine difference formula, this page is open to comments but not edits.

Edit Steps

  1. 1
    First draw your unit circle, label as needed.

  2. 2
    Then label the origin as point z and it has the order pair (0, 0).

  3. 3
    Next label 0 degrees as point y and it has the order pair (1, 0).

  4. 4
    Then draw a special angle from the unit circle and label it angle A this gives us point x which has the order pair (cosA, sinA), you know this because of the definition of the trig functions.

  5. 5
    Next construct another special angle from the unit circle and label it Angle B this gives us point w which has the order pair (cosB, sinB) and point v

  6. 6
    Then construct an angle that is equal to Angle A - Angle B, giving you the angle A-B, this gives you point u which had the order pair (cos(A-B), sin(A-B))

  7. 7
    Then draw a cord going from point u to point y and this creates opposite of angle A-B.

  8. 8
    Next draw a cord going from point w to point x and this also creates the opposite of angle A-B, knowing this information we know that cord uy and cord wx are equivalent.

  9. 9
    Finally use the distance formula Sqrt((x2-x1)^2-(y2-y1)^2) to find the distance between the two points in either cord uy or cord wx.


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Edit Things You'll Need

  • Knowledge of the unit circle.
  • Knowledge of the distance formula.
  • Knowledge of the definition of trig functions.


Edit Related wikiHows


Edit Sources and Citations

Article Info

Categories: Mathematics | Trigonometry

Recent edits by: Ethan Reese

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