OpenEuphoria

Re: trig

• Posted by Evan Marshall <1evan at sbcglobal.net> Apr 18, 2004
• 620 views

cos(u-v) = cos(u)*cos(v) + sin(u)*sin(v)
cos(.5PI-v) = sin(v)
sin(.5PI-u) = cos(u)
sin(-v) = -sin(v)
cos(-v) = -cos(v)
cos(u+v) = cos(u)*cos(v) - sin(u)*sin(v)
sin(u+v) = sin(u)*cos(v) + cos(u)*sin(v)
sin(u-v) = sin(u)*cos(v) - cos(u)*sin(v)
tan(u+v) = (tan(u) + tan(v)) / (1 - tan(u)*tan(v))

equation of a line = y = mx + b

angle(t) between 2 lines:
tan(t) = (m2 - m1) / (1 + m2*m1)

if m2 * m1 = -1 the lines are parallel

sin(2*t) = 2 * sin(t) * cos(t)
cos(2*t) = power(cos(t),2) - power(sin(t),2) = 1 - 2  * 
power(sin(t),2) = 2 * power(cos(t),2) -1
tan(2*t) = 2 * tan(t) / (1 - power(tan(t),2))
power(sin(t),2) = (1 - cos(2*t)) / 2
power(cos(t),2) = (1 + cos(2*t)) / 2
tan(t) = sin(2 * t) / (1 + cos(2*t)) = (1 - cos(2 * t)) / sin(2 * t)

csc(t) = 1 / sin(t)
sec(t) = 1 / cos(t)
cot(t) = 1 / tan(t) = cos(t) / sin(t)
tan(t) = sin(t) / cos(t)
power(cos(t),2) + power(sin(t),2) = 1
power(tan(t),2) + 1 = power(sec(t),2)
power(cot(t),2) + 1 = power(csc(t),2)

sin(u + v) = sin(u) * cos(v) + cos(u) * sin(v)
sin(u - v) = sin(u) * cos(v) - cos(u) * sin(v)
cos(u + v) = cos(u) * cos(v) + sin(u) * sin(v)
cos(u - v) = cos(u) * cos(v) - sin(u) * sin(v)
tan(u + v) = (tan(u) + tan(v)) / (1 - tan(u) * tan(v))
tan(u - v) = (tan(u) - tan(v)) / (1 + tan(u) * tan(v))

power(sin(t),2) = .5 * (1 - cos(2 * t))
power(cos(t),2) = .5 * (1 + cos(2 * t))


sin(u + v) + sin(u - v) = 2 * sin(u) * cos(v)
sin(u + v) - sin(u - v) = 2 * cos(u) * sin(v)
cos(u - v) + cos(u + v) = 2 * cos(u) * cos(v)
cos(u - v) - cos(u + v) = 2 * sin(u) * sin(v)

sin(x) + sin(y) = 2 * sin(.5 * (x + y)) * cos(.5 * (x - y))
sin(x) - sin(y) = 2 * cos(.5 * (x + y)) * sin(.5 * (x - y))
cos(x) + cos(y) = 2 * cos(.5 * (x + y)) * cos(.5 * (x - y))
cos(x) - cos(y) = -2 * sin(.5 * (x + y)) * sin(.5 * (x - y))