sec(t) = 1/cos(t) csc(t) = cosec(t) = 1/sin(t) cos2(t) + sin2(t) = 1 1 + tan2(t) = sec2(t) 1 + cot2(t) = csc2(t)
pi for tan(t) and cot(t)
sin(pi/3) = sqrt(3)/2 cos(pi/3) = 1/2 cos (pi/4) = sin(pi/4) = sqrt(1/2) cos (pi/6) = sqrt(3)/2 sin(pi/6) = 1/2.
sin(t) = sin(t')
cos(t) = -cos(t')
tan(t) = -tan(t')
cot(t) = -cot(t')
t and t' are complementary values <=> t+t' = pi/2.
sin(t) = cos(t')
cos(t) = sin(t')
tan(t) = cot(t')
cot(t) = tan(t')
t and t' are opposite values <=> t+t' = 0.
sin(t) = -sin(t')
cos(t) = cos(t')
tan(t) = -tan(t')
cot(t) = -cot(t')
t and t' are anti-supplementary values <=> t-t' = pi.
sin(t) = -sin(t')
cos(t) = -cos(t')
tan(t) = tan(t')
cot(t) = cot(t')
sin(B) = b/a cos(B) = c/a tan(B) = b/c
cos(C) = b/a sin(C) = c/a tan(C) = c/b
In any triangle:
a b c
------ = ------ = ------
sin(A) sin(B) sin(C)
Cosine rule
a2 = b2 + c2 - 2 b c cos(A)
b2 = c2 + a2 - 2 c a cos(B)
c2 = a2 + b2 - 2 a b cos(C)
Area = (1/2).a.c.sin(B)= (1/2).b.c.sin(A) = (1/2).a.b.sin(C)
cos(u - v) = cos(u).cos(v)+sin(u).sin(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) + tan(v)
tan(u+v) = -----------------
1 - tan(u).tan(v)
tan(u) - tan(v)
tan(u-v) = -----------------
1 + tan(u).tan(v)
sin(2u) = 2sin(u).cos(u)
cos(2u) = cos2 (u) - sin2 (u)
2 tan(u)
tan(2u) = -----------
1- tan2(u)
1 + cos(2u) = 2 cos2 (u) 1 - cos(2u) = 2 sin2 (u)
Let t = tan(u) , then
1 - t2
cos(2u) = --------- ;
1 + t2
2t
sin(2u) = -------- ;
1 + t2
2t
tan(2u) = ------- ;
1 - t2
cos(x) + cos(y) = 2 cos((1/2)(x + y)) cos((1/2)(x - y)) cos(x) - cos(y) = -2 sin((1/2)(x + y)) sin((1/2)(x - y)) sin(x) + sin(y) = 2 sin((1/2)(x + y)) cos((1/2)(x - y)) sin(x) - sin(y) = 2 cos((1/2)(x + y)) sin((1/2)(x - y))
cos(u) = cos(v) <=> (u = v + k.2pi) of (u = -v + k.2pi) sin(u) = sin(v) <=> (u = v + 2.k.pi) of (u = pi - v + 2.k.pi) tan(u) = tan(v) <=> (u = v + k.pi) on condition that tan(u) and tan(v) exist. cot(u) = cot(v) <=> (u = v + k.pi) on condition that cot(u) and cot(v) exist.