Question

Хелпхелпхелп 1) arcsin (-√2/2) + arccos 1/2 2) arcsin √3/2 + arccos √3/2 3) arcsin (-1) + arccos √3/2 4) arccos (-0,5) + arcsin (-0,5) 5) arccos (-√2/2) - arcsin (-1) 6) arccos (-√3/2) + arcsin (-√3/2) 7) arccos √2/2 - arcsin √3/2 8) arctg 1 - arctg √3 9) arctg 1 - arctg (-1) 10) arctg (-√3) + arctg 0 11) arctg 1/√3 + arctg √3 сравните числа: 1) arcsin (-1/2) и arccos √3/2 2) arccos (-1/2) и arctg (-1) 3) arctg √3 и arcsin 1 4) arccos (-√3/2) и arcsin 1/2 уравнения: 1) cos x = √2/2 2) cos x = -1/2 3) cos x = √3/2 4) cos x = -1

Answer 1

1) arcsin (-√2/2) + arccos (1/2) = -pi/4+pi/3 = pi/12
2) arcsin (√3/2) + arccos (√3/2)  = pi/3+pi/6 = pi/2
3) arcsin (-1) + arccos (√3/2) = -pi/2+pi/6 = -pi/3
4) arccos (-0,5) + arcsin (-0,5) = 2pi/3-pi/6 = pi/2
5) arccos (-√2/2) - arcsin (-1) = 3pi/4+pi/2 = 5pi/4
6) arccos (-√3/2) + arcsin (-√3/2) = 5pi/6-pi/3 = pi/2
7) arccos (√2/2) - arcsin (√3/2) = pi/4-pi/3 = -pi/12
8) arctg 1 - arctg √3 = pi/4-pi/3 = -pi/12
9) arctg 1 - arctg (-1) = pi/4+pi/4 = pi/2
10) arctg (-√3) + arctg 0 = -pi/3
11) arctg (1/√3) + arctg √3 = pi/6+pi/3 = pi/2

1) arcsin (-1/2) и arccos (√3/2)
-pi/6 < pi/6
2) arccos (-1/2) и arctg (-1)
2pi/3 > -pi/4
3) arctg √3 и arcsin 1 
pi/3 < pi/2
4) arccos (-√3/2) и arcsin (1/2)
5pi/6 > pi/6

1) cos x = √2/2 
x=pi/4+2pin, x=-pi/4+2pin, n∈Z
2) cos x = -1/2
x=2pi/3+2pin, x=-2pi/3+2pin, n∈Z
3) cos x = √3/2
x=pi/6+2pin, x=-pi/6+2pin, n∈Z
4) cos x = -1
x=pi+2pin, n∈Z