من طرف العلاقات المثلثية
علاقات اساسية
tan(x) = sin(x)/cos(x)
sin²(x) + cos²(x) = 1
sin²(x) = tan²(x) / (1 + tan²(x))
cos²(x) = 1 / (1 + tan²(x))
التحويلات الاساسية
sin(2pi + x) = sin(x)
cos(2pi + x) = cos(x)
tan(2pi + x) = tan(x)
sin( -x) = - sin(x)
cos( -x) = cos(x)
tan( -x) = - tan(x)
sin(pi - x) = sin(x)
cos(pi - x) = - cos(x)
tan(pi - x) = - tan(x)
sin(pi + x) = - sin(x)
cos(pi + x) = - cos(x)
tan(pi + x) = tan(x)
sin(pi/2 - x) = cos(x)
cos(pi/2 - x) = sin(x)
tan(pi/2 - x) = 1/tan(x)
sin(pi/2 + x) = cos(x)
cos(pi/2 + x) = - sin(x)
tan(pi/2 + x) = -1/tan(x)
sin(3pi/2 - x) = - cos(x)
cos(3pi/2 - x) = - sin(x)
tan(3pi/2 - x) = 1/tan(x)
sin(3pi/2 + x) = - cos(x)
cos(3pi/2 + x) = sin(x)
tan(3pi/2 + x) = -1/tan(x)
المعادلات المثلثية
R ينتمى الى k
sin(a) = sin(b)
a = b + 2kpi
a = pi - b + 2kpi
cos(a) = cos(b)
a = b + 2kpi
a = -b + 2kpi
tan(a) = tan(b)
a = b + kpi
علاقات الجمع
sin(a + b) = sin(a)cos(b) + sin(b)cos(a)
sin(a - b) = sin(a)cos(b) - sin(b)cos(a)
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(p) + sin(q) = 2sin((p + q)/2)cos((p - q)/2)
sin(p) - sin(q) = 2sin((p - q)/2)cos((p + q)/2)
cos(p) + cos(q) = 2cos((p + q)/2)cos((p - q)/2)
cos(p) - cos(q) = -2sin((p + q)/2)sin((p - q)/2)
tan(p) + tan(q) = sin(p + q) / (cos(p)cos(q))
tan(p) - tan(q) = sin(p - q) / (cos(p)cos(q))
sin(a)sin(b) = (1/2)(cos(a - b) - cos(a + b))
cos(a)cos(b) = (1/2)(cos(a + b) + cos(a - b))
sin(a)cos(b) = (1/2)(sin(a + b) + sin(a - b))
علاقات اخرى
sin(2a) = 2sin(a)cos(a)
= 2tan(a) / (1 + tan²(a))
cos(2a) = cos²a - sin²a
= 2cos²a - 1
= 1 - 2sin²a
tan(2a) = 2tan(a) / (1 - tan²(a))
sin²(a) = (1 - cos(2a)) / 2
cos²(a) = (1 + cos(2a)) / 2
tan²(a) = (1 - cos(2a)) / (1 + cos(2a))
tan(a) = sin(2a) / (1 + cos(2a))
= (1 - cos(2a)) / sin(2a)
t = tan(a/2) : بوضع
sin(a) = 2t / (1 + t²)
cos(a) = (1 - t²) / (1 + t²)
tan(a) = 2t / (1 - t²)
نظرية موافر
( cos(a) + isin(a))n = cos(na) + isin(na)
نظرية اولر
cos θ = 1/2.(eiθ + e-iθ)
sin θ = 1/(2i).(eiθ - e-iθ)
علاقات اساسية
tan(x) = sin(x)/cos(x)
sin²(x) + cos²(x) = 1
sin²(x) = tan²(x) / (1 + tan²(x))
cos²(x) = 1 / (1 + tan²(x))
التحويلات الاساسية
sin(2pi + x) = sin(x)
cos(2pi + x) = cos(x)
tan(2pi + x) = tan(x)
sin( -x) = - sin(x)
cos( -x) = cos(x)
tan( -x) = - tan(x)
sin(pi - x) = sin(x)
cos(pi - x) = - cos(x)
tan(pi - x) = - tan(x)
sin(pi + x) = - sin(x)
cos(pi + x) = - cos(x)
tan(pi + x) = tan(x)
sin(pi/2 - x) = cos(x)
cos(pi/2 - x) = sin(x)
tan(pi/2 - x) = 1/tan(x)
sin(pi/2 + x) = cos(x)
cos(pi/2 + x) = - sin(x)
tan(pi/2 + x) = -1/tan(x)
sin(3pi/2 - x) = - cos(x)
cos(3pi/2 - x) = - sin(x)
tan(3pi/2 - x) = 1/tan(x)
sin(3pi/2 + x) = - cos(x)
cos(3pi/2 + x) = sin(x)
tan(3pi/2 + x) = -1/tan(x)
المعادلات المثلثية
R ينتمى الى k
sin(a) = sin(b)
a = b + 2kpi
a = pi - b + 2kpi
cos(a) = cos(b)
a = b + 2kpi
a = -b + 2kpi
tan(a) = tan(b)
a = b + kpi
علاقات الجمع
sin(a + b) = sin(a)cos(b) + sin(b)cos(a)
sin(a - b) = sin(a)cos(b) - sin(b)cos(a)
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(p) + sin(q) = 2sin((p + q)/2)cos((p - q)/2)
sin(p) - sin(q) = 2sin((p - q)/2)cos((p + q)/2)
cos(p) + cos(q) = 2cos((p + q)/2)cos((p - q)/2)
cos(p) - cos(q) = -2sin((p + q)/2)sin((p - q)/2)
tan(p) + tan(q) = sin(p + q) / (cos(p)cos(q))
tan(p) - tan(q) = sin(p - q) / (cos(p)cos(q))
sin(a)sin(b) = (1/2)(cos(a - b) - cos(a + b))
cos(a)cos(b) = (1/2)(cos(a + b) + cos(a - b))
sin(a)cos(b) = (1/2)(sin(a + b) + sin(a - b))
علاقات اخرى
sin(2a) = 2sin(a)cos(a)
= 2tan(a) / (1 + tan²(a))
cos(2a) = cos²a - sin²a
= 2cos²a - 1
= 1 - 2sin²a
tan(2a) = 2tan(a) / (1 - tan²(a))
sin²(a) = (1 - cos(2a)) / 2
cos²(a) = (1 + cos(2a)) / 2
tan²(a) = (1 - cos(2a)) / (1 + cos(2a))
tan(a) = sin(2a) / (1 + cos(2a))
= (1 - cos(2a)) / sin(2a)
t = tan(a/2) : بوضع
sin(a) = 2t / (1 + t²)
cos(a) = (1 - t²) / (1 + t²)
tan(a) = 2t / (1 - t²)
نظرية موافر
( cos(a) + isin(a))n = cos(na) + isin(na)
نظرية اولر
cos θ = 1/2.(eiθ + e-iθ)
sin θ = 1/(2i).(eiθ - e-iθ)
