Question

Решитеsin(x/3+1)=-1​

Answer 1

Sin(x/3+1)=-1

x/3+1=-π/2+2πk

x/3=-1-π/2+2πk

x=-3-3π/2+6πk;k€Z

Answer 2

To solve the equation sin(x/3 + 1) = -1, we need to find the values of x that satisfy this equation. Remember that the sine function oscillates between -1 and 1, and we're looking for the values of x that make sin(x/3 + 1) equal to -1.

First, let's find the general form of the equation:

sin(x/3 + 1) = -1

To find the solutions, we need to isolate x. Follow these steps:

Step 1: Subtract 1 from both sides to move the constant to the other side of the equation:

sin(x/3 + 1) - 1 = 0

Step 2: Now, we can use the identity sin(a) - 1 = -sin(a + π/2). So, our equation becomes:

-sin(x/3 + 1 + π/2) = 0

Step 3: Divide both sides by -1 to get rid of the negative sign:

sin(x/3 + 1 + π/2) = 0

Step 4: Now, we need to find the values of x/3 + 1 + π/2 that make the sine function equal to zero. The sine function is equal to zero at integer multiples of π:

x/3 + 1 + π/2 = nπ, where n is an integer

Step 5: Now, solve for x:

x/3 = nπ - 1 - π/2

x = 3(nπ - 1 - π/2)

x = 3nπ - 3 - 3π/2

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

x = 3nπ - 3 - 3π/2, where n is an integer.

This equation represents an infinite number of solutions for different integer values of n. Each value of n will give a different value of x that satisfies the original equation.