1 − − −1 − − −1 0 sinϕ 0 1 0 −1 − − −1

ϕ
0
cos ϕ 1
sin ϕ
0
π
6
√
3
2
π
4
√
2
2
√
2
2
1
2
π
3
π
2
2π
3
1
2
√
3
2
0
− 12
√
1
3
2
3π
4
√
−
√
2
2
2
2
5π
6
√
3
2
−
7π
6
√
π
−1 −
1
2
5π
4
√
3
2
2
2
√
− 22
−
− 21
0
4π
3
3π
2
5π
3
− 12
0
1
2
√
√
−
3
2
−1 −
3
2
7π
4
√
2
2
√
−
2
2
11π
6
√
3
2
− 12
sin x
cos x
, ctg x =
, sin (x + 2kπ) = sin x, cos (x + 2kπ) = cos x,
cos x
sin x
tg (x + kπ) = tg x, ctg (x + kπ) = ctg x, where k is an integer number;
tg x =
sin2 x + cos2 x = 1, sin 2x = 2 sin x cos x,
cos 2x = cos2 x − sin2 x.
INTEGRALS
DERIVATIVES
R
0 dx = C
R
dx = x + C
R
xα dx =
0
(c) = 0
α 0
(x ) = αx
x 0
(e ) = e
α−1
x
x 0
R 1
x
x
(a ) = a ln a
0
(ln x) =
1
x
0
(loga x) =
xα+1
α+1
+ C for α 6= −1
dx = ln |x| + C
R x
e dx
= ex + C
ax
ln a
R
ax dx =
R
sin x dx = − cos x + C
R
cos x dx = sin x + C
R
1
sin2 x
dx = − ctg x + C
R
1
cos2 x
dx = tg x + C
R
dx = arc tg x + C
√ 1
1−x2
1
1+x2
R
1
− √1−x
2
√ 1
1−x2
R
sh x dx = ch x + C
R
ch x dx = sh x + C
R
1
sh2 x
dx = −cth x + C
R
1
ch2 x
dx = th x + C
1
x ln a
+C
0
(sin x) = cos x
(cos x)0 = − sin x
0
(tg x) =
1
cos2 x
0
(ctg x) =
− sin12 x
(arc sin x)0 =
0
(arc cos x) =
0
(arc tg x) =
1
1+x2
1
(arc ctg x)0 = − 1+x
2
0
(sh x) = ch x
0
(ch x) = sh x
√
dx = ln x + x2 + k + C,
√
√
R√
x2 + k dx = x2 x2 + k + k2 ln x + x2 + k + C
√
R√
2
x
+C
a2 − x2 dx = x2 a2 − x2 + a2 arc sin |a|
R
(th x)0 =
1
ch2 x
(cth x)0 = − sh12 x
dx = arc sin x + C
√ 1
x2 +k