أظن أن أغلبية الطلبة يحتاجون إلى هذه العلاقات وبخصوص طلبة شعبة الرياضيات

علاقات أساسية
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 الأساسية
sin(2 + x) = sin(x).....cos(2 + x) = cos(x)....tan(2 + x) = tan(x)....sin( -x) = - sin(x)....cos( -x) = cos(x)
tan( -x) = - tan(x)....sin( - x) = sin(x)...cos( - x) = - cos(x)....tan( - x) = - tan(x)....sin( + x) = - sin(x)
cos( + x) = - cos(x)....tan( + x) = tan(x)....sin( /2 - x) = cos(x)....cos( /2 - x) = sin(x)....tan( /2 - x) = 1/tan(x)
sin( /2 + x) = cos(x).....cos( /2 + x) = - sin(x)........tan( /2 + x) = -1/tan(x)........
sin(3 /2 - x) = - cos(x)cos(3 /2 - x) = - sin(x)....tan(3 /2 - x) = 1/tan(x)....sin(3 /2 + x) = - cos(x)
cos(3 /2 + x) = sin(x)........tan(3 /2 + x) = -1/tan(x)

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)

علاقات أخرى
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 أولر
cos θ = 1/2.(eiθ + e-iθ).....................sin θ = 1/(2i).(eiθ - e-iθ)