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TRIGONOMETRY - Coggle Diagram

- - - - sin 45 = √2/2
      - cos 45 = √2/2
      - tan 45 = 1
  - - - sin 30 = 1/2
      - cos 30 = √3/2
      - tan 30 = √3/3
      - sin 60 = √3/2
      - cos 60 = 1/2
      - tan 60 =√3
- - - - two angles and length of one side
      - length of two sides and a non-included angle
  - - - length of three sides
      - length of two sides and an included angle
- - - - Domain : x ∈ R
      - Range : -1 ≤ y ≤ 1
      - Period : 2π
    - - Domain : x ∈ R
      - Range : -1 ≤ y ≤ 1
      - Period : 2π
    - - Domain : x ∈ R / { π/2 + πn, n ∈ Z}
      - Range : y ∈ R
      - Period : π
      - Vertical asymptotes : π/2 + πn, n ∈ R
    - - Domain : x ∈ R / { πn, n ∈ Z}
      - Range : y ≤ -1 , y ≥ 1
      - Period : 2π
      - Vertical asymptotes : πn, n ∈ Z
    - - Domain : x ∈ R / { π/2 + πn, n ∈ Z}
      - Range : y ≤ -1, y ≥ 1
      - Period : 2π
      - Vertical asymptotes : π/2 + πn, n ∈ Z
    - - Domain : x ∈ R / { πn, n ∈ z}
      - Range : y ∈ R
      - Period : π
      - Vertical asymptotes : πn, n ∈ R
        Point of discontinuity : { π/2 + πn, n ∈ Z}
- - - - f(x) = sin x
        Domain : { -π/2 ≤ x ≤ π/2 }
        Range : { -1 ≤ y ≤ 1 }
      - f(x) = arcsin x
        Domain : { -1 ≤ x ≤ 1 }
        Range : { -π/2 ≤ y ≤ π/2 }
    - - f(x) = cos x
        Domain : { 0 ≤ x ≤ π }
        Range : { -1 ≤ y ≤ 1 }
      - f(x) = arccos x
        Domain : { -1 ≤ x ≤ 1 }
        Range : { 0 ≤ y ≤ π }
    - - f(x) = tan x
        Domain : { -π/2 ≤ x ≤ π/2 }
        Range : y ∈ R
      - f(x) = arctan x
        Domain : x ∈ R
        Range : { -π/2 ≤ y ≤ π/2 }
    - - f(x) = csc x
        Domain : { -π/2 ≤ x ≤ π/2 } / {0}
        Range : y ≤ -1 , y ≥ 1
      - f(x) = arccsc x
        Domain : x ≤ -1 , x ≥ 1
        Range : { -π/2 ≤ x ≤ π/2 } / {0}
    - - f(x) = sec x
        Domain : { 0 ≤ x ≤ π } / { π/2 }
        Range : y ≤ -1 , y ≥ 1
      - f(x) = arcsec x
        Domain : x ≤ -1 , x ≥ 1
        Range : { 0 ≤ y ≤ π } / { π/2 }
    - - f(x) = cot x
        Domain : { 0 ≤ x ≤ π }
        Range : y ∈ R
      - f(x) = arccot x
        Domain : x ∈ R
        Range : { 0 ≤ y ≤ π }
- - - - sin (A+B) = sin A cos B + cos A sin B
      - sin (A-B) = sin A cos B - cos A sin B
      - cos (A+B) = cos A cos B - sin A sin B
      - cos (A-B) = cos A cos B + sin A sin B
      - tan (A+B) = (tan A + tan B) / (1 - tan A tan B)
      - tan (A-B) = (tan A - tan B) / (1+ tan A tan B)
    - - sin 2A = 2 sin A cos A
      - cos 2A = cos²A - sin²A
        cos 2A = 1 - 2 sin²A
        cos 2A = 2 cos²A - 1
      - tan 2A = (2 tan A) / (1 - tan²A)
    - - sin A = 2 sin (A/2) cos (A/2)
      - cos A = cos²(A/2) - sin²(A/2)
        cos A = 1 - 2 sin²(A/2)
        cos A = 2 cos²(A/2) - 1