MATHEMATICS
{trigonometry}
Law of Sines
a = b = c
sin A sin B sin C
TRIGONOMETRIC RATIOS
sin (A+B) = sin A cos B + cos A sin B
sin (A-B) = sin A cos B - cos A sin B
cos (A+B) = cos A cos B - sin A sin B
cos (A-B) = cos A cos B + sin A sin B
B
Law of Cosines
a2 = b2+c2-2bc(cos A)
b2 = a2+c2-2ac(cos B)
c2 = a2+b2-2ab(cos C)
tan A + tan B
1 - tan A tan B
tan A - tan B
tan (A-B) =
1 + tan A tan B
sinθ
tanθ =
cosθ
tan (A+B) =
c
a
Law of Tangents
a-b = tan 1/2(A-B)
a+b
tan 1/2(A+B)
b-c = tan 1/2(B-C)
b+c tan 1/2(B+C)
sin2θ + cos2θ = 1
cos2θ - sin2θ = cos2θ
tan2θ+1 = sec2θ
cot2θ+1 = csc2θ
A
c-a = tan 1/2(C-A)
c+a tan 1/2(C+A)
C
b
45º
1
2
60º
2
a (adjacent)
3
1
sin 45º =
1
2
cos 45º =
1
2
1
sin 30º = 2
3
sin 60º = 2
sinθ =
3
cos 30º = 2
1
cos 60º = 2
cosθ =
1
tan 30º = 3
tan 60º = 3
tanθ =
DO NOTSUBMI
T
FOR PRI
NT
tan 45º = 1
π/2
π
3π/2
2π
sinθ
0
1
0
−1
0
cosθ
1
0
−1
0
1
tanθ
0
∞
0
−∞
0
(sin/cos)
o (opposite)
1
=
h (hypotenuse)
cscθ
a (adjacent) = 1
h (hypotenuse)
secθ
1
o (opposite)
a (adjacent) = cotθ
y
VALUES OF TRIGONOMETRIC RATIOS
0
h
h(
30º
45º
θ
te
ypo
)
se
nu
1
r
θ
r
r
x
θ = 1 radian
π radians = 180º
2π radians = 360º
QUADRANTS
secθ
1
∞
−1
∞
1
cscθ
∞
1
∞
−1
∞
cotθ
∞
0
−∞
0
∞
(1/cos)
(1/sin)
(1/tan)
note: ∞ denotes undefined or infinite
Quad II
90º-180º
sin, csc are +
Quad I
0º-90º
all ratios are +
Quad III
180º-270º
tan, cot are +
Quad IV
270º-360º
cos, sec are +
o (opposite)
REVI
EW ONLY