Question

Знайти ривняння, що маэ корени: 1)arccosx=-П/3, 2)arcsinx=П, 3)arctgx=2, 4)arcctgx=3.

Answer 1

1)arccosx=-π/3 ;arccosx€[0;π]
нет решения
2)arcsinx=π
arcsinx€[-π/2;π/2]
нет решения
3)arctgx=2
x=tg2
4)arcctgx=3
x=tg3

Answer 2

1. arccos(x) = -π/3

To find the equation with roots, we can rewrite the equation in exponential form:

x = cos(-π/3)

Using the properties of the cosine function, we know that cos(-θ) = cos(θ). Therefore:

x = cos(π/3)

Now, the equation can be written as:

cos(π/3) - x = 0

2. arcsin(x) = π

Similar to the previous equation, we can rewrite it using exponential form:

x = sin(π)

The equation becomes:

sin(π) - x = 0

3. arctan(x) = 2

Rewriting in exponential form:

x = tan(2)

The equation can be written as:

tan(2) - x = 0

4. arccot(x) = 3

In exponential form:

x = cot(3)

The equation becomes:

cot(3) - x = 0

These are the equations corresponding to the given conditions.