trigonometry math is beautiful. is it? well, if its not nice, than its damn sure of a very b.i.g....
TRANSCRIPT
Trigonometry
Math is beautiful.
Is it?
Well, if it’s not nice, than it’s 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
rO
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 valuesr, a, b, B
Values to be foundc, 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