sin x = a/c
cos x = b/c
tg x = a/b=sinx/cos x
ctg x = b/a = cos x/sin x
sin (p -a ) = sin a
sin (p /2 -a ) = cos a
cos (p /2 -a ) = sin a
cos (a + 2p k) = cos a
sin (a + 2p k) = sin a
tg (a + p k) = tg a
ctg (a + p k) = ctg a
sin² a + cos² a =1
ctg a = cosa / sina , a ¹ p n, nÎ Z
tga × ctga = 1, a ¹ (p n)/2, nÎ Z
1+tg² a = 1/cos² a , a ¹ p (2n+1)/2
1+ ctg² a =1/sin² a , a ¹ p n
Формулы сложения:
sin(x+y) = sin x cos y + cos x sin y
sin (x-y) = sin x cos y - cos x sin y
cos (x+y) = cos x cos y - sin x sin y
cos (x-y) = cos x cos y + sin x sin y
tg(x+y) = (tg x + tg y)/ (1-tg x tg y )
x, y, x + y ¹ p /2 + p n
tg(x-y) = (tg x - tg y)/ (1+tg x tg y)
x, y, x - y ¹ p /2 + p n
Формулы двойного аргумента.
sin 2a = 2sin a cos a
cos 2a = cos² a - sin² a = 2 cos² a - 1 =
= 1-2 sin² a
tg 2a = (2 tga )/ (1-tg² a )
1+ cos a = 2 cos² a /2
1-cosa = 2 sin² a /2
tga = (2 tg (a /2))/(1-tg² (a /2))