Question

Sinx>0.5 Как записать решение?

Answer 1

X∈(Pi/6;5pi/6)
..............................

Answer 2

To express the solution to the inequality sin(x) > 0.5, you need to find the range of values for which the sine of x is greater than 0.5.

The sine function varies between -1 and 1 on the unit circle. When sin(x) > 0.5, it means that x is in the first and second quadrants of the unit circle, where the y-coordinate of the point on the unit circle is greater than 0.5.

To express the solution, you can use interval notation:

Solution: x ∈ (a, b)

In interval notation, (a, b) denotes an open interval, meaning that the values of x are greater than a and less than b, but excluding a and b themselves.

Now, we need to find the values of a and b that satisfy sin(x) > 0.5.

Step 1: Find the angle whose sine is 0.5: The angle whose sine is 0.5 is π/6 (30 degrees) in the first quadrant.

Step 2: Find the angle whose sine is -0.5: The angle whose sine is -0.5 is -π/6 (-30 degrees) in the second quadrant.

Step 3: Write the solution using interval notation: Since the sine function has a period of 2π (360 degrees), we can generalize the solution as follows:

x ∈ (π/6 + 2nπ, π/2 + 2nπ) and x ∈ (3π/2 + 2nπ, 11π/6 + 2nπ)

where n is an integer that can be any positive or negative whole number (including zero). The 2nπ term accounts for the periodicity of the sine function.

This means that any value of x that falls within these intervals will satisfy the inequality sin(x) > 0.5.