Question

При каких значениях аргумента функция y=sinx принимает значение 1/2 на интервале (-П:+П) ?

Answer 1

$\sin x=\cfrac{1}{2}\\x=\cfrac{\pi}{6}+2\pi n, n\in \mathbb{Z}\\x=\cfrac{5\pi}{6}+2\pi n, n\in \mathbb{Z}$
Получаем $\cfrac{\pi}{6}\phantom{g}; \cfrac{5\pi}{6}$

Answer 2

Sinx=1/2
$x_1=\frac{\pi}{6}, x_2=\frac{5\pi}{6} ,\\x_1,x_2 \in (-\pi,\pi )$

Answer 3

Finding the Values of x for y = sin(x) = 1/2

To find the values of x for which the function y = sin(x) takes the value 1/2 on the interval (-π, π), we can use the properties of the sine function and its periodic nature.

The function y = sin(x) has a period of 2π, which means it repeats every 2π units along the x-axis. The function achieves its maximum value of 1 at π/2 and its minimum value of -1 at -π/2. Therefore, the function y = sin(x) = 1/2 at two points within the interval (-π, π).

Solution

The values of x for which y = sin(x) = 1/2 on the interval (-π, π) are: - x = π/6 - x = 5π/6

This can be verified by using the properties of the sine function and its periodic nature.

Explanation

The sine function, y = sin(x), has a range of [-1, 1]. This means it oscillates between -1 and 1. The function achieves its maximum value of 1 at π/2 and its minimum value of -1 at -π/2. Therefore, the function y = sin(x) = 1/2 at two points within the interval (-π, π).

Conclusion

The values of x for which the function y = sin(x) takes the value 1/2 on the interval (-π, π) are x = π/6 and x = 5π/6.