Trigonometry Math is beautiful. Is it? Well, if its not nice, than its damn sure of a very B.I.G. HELP.

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Presentation transcript:

Trigonometry Math is beautiful. Is it? Well, if its not nice, than its damn sure of a very B.I.G. *HELP*.

Trigonometry Rotation of any object in an orthogonal system is done very easy using trigonometry. Trigonometry is all about the circle having a radius of 1 unit in length. We will rapidly show the theory behind using this circle.

Trigonometry The formula we will determine is useful in rotating a point x by a number of degrees/ radians from its initial position around a center O. You need to know the initial coordinates of x and the angle by which the point must be rotated around O.

Trigonometry r O r = 1 x(a, b) A a = r * cos(A) b = r * sin(A) B x(c, d) c = r * cos(A + B) d = r * sin(A + B) Known values r, a, b, B Values to be found c, d

Trigonometry cos(A + B) = cos(A)cos(B) - sin(A)sin(B) sin(A + B) = sin(A)cos(B) + cos(A)sin(B) r * cos(A + B) = r * (cos(A)cos(B) - sin(A)sin(B)) = = r * cos(A)cos(B) – r * sin(A)sin(B) r * sin(A + B) = r * (sin(A)cos(B) + cos(A)sin(B)) = = r * sin(A)cos(B) + r * cos(A)sin(B) a = r * cos(A) ; b = r * sin(A) ; r = 1 c = r * cos(A + B) d = r * sin(A + B)

Trigonometry cos(A + B) = cos(A)cos(B) - sin(A)sin(B) sin(A + B) = sin(A)cos(B) + cos(A)sin(B) r * cos(A + B) = r * cos(A)cos(B) – r * sin(A)sin(B) r * sin(A + B) = r * sin(A)cos(B) + r * cos(A)sin(B) a = r * cos(A) ; b = r * sin(A) ; r = 1 c = r * cos(A + B) d = r * sin(A + B)

Trigonometry cos(A + B) = cos(A)cos(B) - sin(A)sin(B) sin(A + B) = sin(A)cos(B) + cos(A)sin(B) r * cos(A + B) = r * cos(A)cos(B) – r * sin(A)sin(B) r * sin(A + B) = r * sin(A)cos(B) + r * cos(A)sin(B) a = r * cos(A) ; b = r * sin(A) ; r = 1 c = r * cos(A + B) d = r * sin(A + B)

Trigonometry cos(A + B) = cos(A)cos(B) - sin(A)sin(B) sin(A + B) = sin(A)cos(B) + cos(A)sin(B) r * cos(A + B) = a * cos(B) – r * sin(A)sin(B) r * sin(A + B) = r * sin(A)cos(B) + a * sin(B) a = r * cos(A) ; b = r * sin(A) ; r = 1 c = r * cos(A + B) d = r * sin(A + B)

Trigonometry cos(A + B) = cos(A)cos(B) - sin(A)sin(B) sin(A + B) = sin(A)cos(B) + cos(A)sin(B) r * cos(A + B) = a * cos(B) – r * sin(A)sin(B) r * sin(A + B) = r * sin(A)cos(B) + a * sin(B) a = r * cos(A) ; b = r * sin(A) ; r = 1 c = r * cos(A + B) d = r * sin(A + B)

Trigonometry cos(A + B) = cos(A)cos(B) - sin(A)sin(B) sin(A + B) = sin(A)cos(B) + cos(A)sin(B) r * cos(A + B) = a * cos(B) – b * sin(B) r * sin(A + B) = b * cos(B) + a * sin(B) a = r * cos(A) ; b = r * sin(A) ; r = 1 c = r * cos(A + B) d = r * sin(A + B)

Trigonometry cos(A + B) = cos(A)cos(B) - sin(A)sin(B) sin(A + B) = sin(A)cos(B) + cos(A)sin(B) r * cos(A + B) = a * cos(B) – b * sin(B) r * sin(A + B) = b * cos(B) + a * sin(B) a = r * cos(A) ; b = r * sin(A) ; r = 1 c = r * cos(A + B) d = r * sin(A + B)

Trigonometry cos(A + B) = cos(A)cos(B) - sin(A)sin(B) sin(A + B) = sin(A)cos(B) + cos(A)sin(B) c = a * cos(B) – b * sin(B) r * sin(A + B) = b * cos(B) + a * sin(B) a = r * cos(A) ; b = r * sin(A) ; r = 1 c = r * cos(A + B) d = r * sin(A + B)

Trigonometry cos(A + B) = cos(A)cos(B) - sin(A)sin(B) sin(A + B) = sin(A)cos(B) + cos(A)sin(B) c = a * cos(B) – b * sin(B) r * sin(A + B) = b * cos(B) + a * sin(B) a = r * cos(A) ; b = r * sin(A) ; r = 1 c = r * cos(A + B) d = r * sin(A + B)

Trigonometry cos(A + B) = cos(A)cos(B) - sin(A)sin(B) sin(A + B) = sin(A)cos(B) + cos(A)sin(B) c = a * cos(B) – b * sin(B) d = b * cos(B) + a * sin(B) a = r * cos(A) ; b = r * sin(A) ; r = 1 c = r * cos(A + B) d = r * sin(A + B)

Trigonometry cos(A + B) = cos(A)cos(B) - sin(A)sin(B) sin(A + B) = sin(A)cos(B) + cos(A)sin(B) c = a * cos(B) – b * sin(B) d = b * cos(B) + a * sin(B) a = r * cos(A) ; b = r * sin(A) ; r = 1 c = r * cos(A + B) d = r * sin(A + B)

Trigonometry c = a * cos(B) – b * sin(B) d = b * cos(B) + a * sin(B) (c, d) pair represents the coordinates of x that is actually x after the rotation