Question

Sin5x=1 решите пожалуйста

Answer 1

Sin 5x=1
5x=pi/2+2piN
x=pi/10+2/5*piN

Answer 2

sin5x=1 
X=PI/10±п/15+2/5пn

Answer 3

Solving the Equation sin(5x) = 1

To solve the equation sin(5x) = 1, we need to find the values of x that satisfy this equation. Let's break down the steps to solve it:

1. Start by isolating sin(5x) on one side of the equation. Subtract 1 from both sides: sin(5x) - 1 = 0

2. Now, we need to find the values of x that make sin(5x) - 1 equal to zero. This means we are looking for the x-values where sin(5x) is equal to 1.

3. To find these values, we can use the inverse sine function (also known as arcsin or sin^(-1)). Applying the inverse sine function to both sides of the equation, we get: arcsin(sin(5x) - 1) = arcsin(0)

4. The inverse sine of 0 is 0, so the equation simplifies to: arcsin(sin(5x) - 1) = 0

5. Now, we need to solve for 5x. Take the sine of both sides of the equation: sin(arcsin(sin(5x) - 1)) = sin(0)

6. The sine of arcsin is the argument itself, so the equation becomes: sin(5x) - 1 = 0

7. Add 1 to both sides of the equation: sin(5x) = 1

8. We have now arrived back at the original equation. This means that the equation sin(5x) = 1 has infinitely many solutions. The solutions can be expressed as: 5x = π/2 + 2πn, where n is an integer.

9. To find the values of x, divide both sides of the equation by 5: x = (π/2 + 2πn)/5, where n is an integer.

Therefore, the solutions to the equation sin(5x) = 1 are given by x = (π/2 + 2πn)/5, where n is an integer.

Please note that this solution assumes we are working in radians. If we are working in degrees, the values of π/2 and 2π should be replaced with 90° and 360°, respectively.

I hope this helps! Let me know if you have any further questions.