I.
, ,
1. . 1 , .
180=π ; n π n
180 .
b
a
:
sin a = ; tg a = ; ctg a = .
:
= 1;
tg a = ctg a = ;
tg a ctg a = 1;
a + 1 = ;
a + 1 = .
:
cos (α ß) = cos α cos ß + sin α sin ß;
cos (α + ß) = cos α cos ß - sin α sin ß;
sin (α ß) = sin α cos ß- cos α sin ß;
sin (α + ß) = sin α cos ß + cos α sin ß;
= ;
= .
y y
x x
y
x
():
+ sin = 2 sin cos ;
- sin = 2 sin cos ;
+ cos = 2 cos cos ;
- cos = - 2 sin sin .
:
sin 2 = 2 sin cos ;
cos 2 = -
cos 2 = ;
cos 2 = ;
tg 2 .
:
= sin ;
= .
.
1. , :
) sin a = 0,8 < a <
) cos a = < a < ;
) sin a = 0 < a < ;
) cos a = < a < .
2. :
) ;
) ;
)
) +
3. :
a) ;
+ =2.
II.
,
[ ], .
. rcsin
rcsin = , sin = [ ].
[0 ], .
. arccos = , cos = [0 ].
, .
. arctg = , tg = 1
[0 ], .
. arcctg = , ctg = [0 ]
.
4. :
4.1. ) arcsin 0 + arccos 0;
) arcsin + arccos ;
) arcsin + arccos ;
) arcsin ( 1) + arccos .
4.2. ) arccos ( 0,5) + arcsin ( 0,5);
) arccos arcsin ();
) arccos arcsin
) arccos arcsin .
4.3. ) arctg 1 arctg
) arctg 1 arctg ();
) arctg + arctg 0;
) arctg .
cos t = a (1)
( > 1, )
|
|
(1): t = arccos a + 2 , n Z (2)
( ≤ 1)
(1) a = 1 a = 0:
cos t = 1 t = + 2 , n Z
cos t = t = + , n Z
1. cos x =
(2) x = arccos + 2 , n Z
sin t = a (3)
( > 1, ≤ 1 t)
(3) , : \
t = ( 1) ᵏ + , k Z (4)
sin t = 1
t = + 2 , n Z.
= 1 = 0 :
sin t = 1, t = + 2 , n Z.
sin t = 0, t = , n Z.
2. : sin x = . (4)
= ( 1) ᵏ arcsin + , k Z, ..
= ( 1) ᵏ + , k Z.
tg t = a (5)
t = arctg a + , n Z. (6)
3. : tg = . (6)
= + , n Z, = , :
x = + , n Z.
.
5. :
) sin =
) tg ( 4x) = ;
) cos ( x ) = ;
) ctg = 1.