Question

Sin(x/3 + pi/18) = - 1

Answer 1

Розв'язок:

sin(x/3+π/18) = -1

x/3+π/18 = arcsin(-1)+πn, n є Z.

x/3+π/18 = 3π/2+2πn, n є Z.

x/3 = 3π/2-π/18+2πn, n є Z.

x/3 = (27π-π)/18+2πn, n є Z.

x/3 = 26π/18+2πn, n є Z.

x/3 = 13π/9+2πn, n є Z.

x = 13π/3+6πn, n є Z.

Відповідь: 13π/3+6πn, n є Z.

Answer 2

To solve the equation sin(x/3 + π/18) = -1, you can follow these steps:

1. First, let's find the general solution for sin(x/3 + π/18) = -1. To do this, we need to find the values of x that satisfy this equation.

2. Since sin(-π/2) = -1, we can write the equation as:

   sin(x/3 + π/18) = sin(-π/2)

3. Now, we have:

   x/3 + π/18 = -π/2

4. Solve for x:

   x/3 = -π/2 - π/18

   x/3 = (-9π/18) - (π/18)

   x/3 = -10π/18

   x/3 = -(5/9)π

5. Multiply both sides by 3 to isolate x:

   x = -3 * (5/9)π

6. Simplify:

   x = -(5/3)π

So, the general solution to the equation sin(x/3 + π/18) = -1 is:

x = -(5/3)π + 2nπ, where n is an integer.

This equation represents all the values of x that satisfy the given equation. You can choose different integer values for n to find specific solutions within a certain range.