Question

Sin(x/3+П/6)=1 ПОМОГИТЕ

Answer 1

Sin(x/3+π/6)=1
sin(π/2)=1  ⇒    x/3+π/6=π/2
                          x/3=π/2-π/6
                          x/3=2π/6=π/3
                          x=3π/3=π
Ответ: x=π

Answer 2

Solving the Equation sin(x/3+π/6)=1/2

To solve the equation sin(x/3+π/6)=1/2, we can use the trigonometric identity for sin(x+y) which states that sin(x+y) = sin(x)cos(y) + cos(x)sin(y). Let's solve for x.

Using the trigonometric identity, we have: sin(x/3+π/6) = sin(x/3)cos(π/6) + cos(x/3)sin(π/6)

We know that sin(π/6) = 1/2 and cos(π/6) = √3/2.

Substituting these values, we get: sin(x/3+π/6) = (1/2)cos(x/3) + (√3/2)sin(x/3)

Now, we need to solve for x. Let's proceed to solve for x using this equation.

Solving for x

To solve for x, we can use the fact that sin(x) = 1/2 when x = π/6 + 2πn or x = 5π/6 + 2πn, where n is an integer. Let's find the values of x based on this information.

The solutions for x are: - x = π/6 + 2πn - x = 5π/6 + 2πn

These are the values of x that satisfy the equation sin(x/3+π/6) = 1/2.

I hope this helps! If you have any further questions, feel free to ask.