Laws Flashcards
1
Q
cosA
A
b²+c²-a²
2bc
2
Q
cosB
A
c²+a²-b²
2ca
3
Q
cosC
A
a²+b²-c²
2ab
4
Q
a
A
bcosC + ccosB
5
Q
b
A
ccosA + acosC
6
Q
c
A
acosB + bcosA
7
Q
tan(B-C)/2
A
(b-c)/(b+c) × cot(A/2)
8
Q
tan(C-A)/2
A
(c-a)/(c+a) × cot(B/2)
9
Q
tan(A-B)/2
A
(a-b)/(a+b) × cot(C/2)
10
Q
sin(A/2)
A
√{(s-b)(s-c)/bc)}
11
Q
sin(B/2)
A
√{(s-c)(s-a)/ca}
12
Q
sin(C/2)
A
√{(s-a)(s-b)/ab}
13
Q
cos(A/2)
A
√{s(s-a)/bc}
14
Q
cos(B/2)
A
√{s(s-b)/ca}
15
Q
cos(C/2)
A
√{s(s-c)/ab}
16
Q
tan(A/2)
A
√{(s-b)(s-c)/s(s-a)}
17
Q
tan(B/2)
A
√{(s-c)(s-a)/s(s-b)}
18
Q
tan(C/2)
A
√{(s-a)(s-b)/s(s-c)}
19
Q
∆
A
1/2 × (product of any two sides) × (sine of the included angle)
e.g.
1/2 × bc sinA
20
Q
∆ in terms of sides
A
(1/4) × {2a²b² + 2b²c² + 2c²a² - a⁴ - b⁴ - c⁴} ^½
21
Q
∆ in terms of s
A
√{s(s-a)(s-b)(s-c)}
