Miscellaneous Math Flashcards
1
Q
Common sets of interest include:
A
- R—the real numbers;
- R+—the non-negative real numbers (includes zero);
- R^2—the ordered pairs in the real 2D plane;
- R^n—the points in n-dimensional Cartesian space;
- Z—the integers;
- S^2—the set of 3D points (points in R3) on the unit sphere
2
Q
Differentiate loga x
A
d/dx loga x = 1/x ln a
3
Q
Differentiate a^x
A
d/dx a^x = a^x ln a.
4
Q
Sec and tan identity
A
sec2 A − tan2 A = 1
5
Q
cosec and cot identity
A
csc2 A − cot2 A = 1
6
Q
Product identities for sinAsinB
A
sin A sin B = −(cos(A + B) − cos(A − B))/2
7
Q
Product identities for sinAcosB
A
sin A cos B = (sin(A + B) + sin(A − B))/2
8
Q
Product identities for cosAcosB
A
cos A cos B = (cos(A + B) + cos(A − B))/2
9
Q
Law of tangents
A
(a + b)/(a − b) = tan ((A+B)/2) / tan ((A−B)/2)
10
Q
Area of triangle formula with square root
A
triangle area = 1/2 x ((a + b + c)(−a + b + c)(a − b + c)(a + b − c))^0.5
11
Q
Dot product formula
A
a · b = |a| x |b| x cos φ
