Download Collection of formulas to the course Basic Mathematics

Linnaeus University
School of Computer Science, Physics and Mathematics
Collection of formulas to the course Basic Mathematics
Trigonometric formulas
sin(−x) = − sin x
sin(π − x) = sin x
sin(π/2 − x) = cos x
sin(x + y) = sin x cos y + cos x sin y
sin x
cos x
cos(−x) = cos x
cos(π − x) = − cos x
cos(π/2 − x) = sin x
cos(x + y) = cos x cos y − sin x sin y
sin 2x = 2 sin x cos x
1 − cos 2x
sin2 x =
2
cos 2x = 2 cos2 x − 1 = 1 − 2 sin2 x = cos2 x − sin2 x
1 + cos 2x
cos2 x =
2
sin2 x + cos2 x = 1
tan x =
x
0
cos x
1
sin x
0
π
6
√
3
2
1
2
π
4
π
3
1
√
2
1
√
2
1
√2
3
2
π
2
π
0
−1
1
0
Exponential and logarithmic identities
If
a, b > 0 then:
a0 = 1
ax+y = ax · ay
(ax )y = axy
(a · b)x = ax · bx
ax
ax−y = y
a x aax
= x
b
b
a > 0, a 6= 1 then:
a
a
log 1 = 0
log(x · y) =a log x +a log y
x
a
a
log( ) =a log x −a log y
log(xy ) = y a log x
y
Factorial and binomial coefficient
For each integer n = 1, 2, 3, . . . is n! = n(n − 1) · · · 3 · 2 · 1. For n = 0 we define 0! = 1.
n!
For all integers n, k where 0 ≤ k ≤ n is nk = k!(n−k)!
If
Binomial theorem
For each natural number n:
n X
n n−k k
n n 0
n n−1 1
n n−2 2
n 0 n
n
(x + y) =
x y =
x y +
x y +
x y + ··· +
xy
k
0
1
2
n
k=0
Polar form
Every complex number z = x + iy can be expressed as z = r(cos φ + i sin φ). Using Euler’s
formula this can be written as z = reiφ .