Question

Решите уравнение 2sinx-1=0 У меня получилось так: 2sinx=1 Sinx=1/2 Чему равен sinx=1/2?

Answer 1

Sinx=1/2
Это простейшее тригонометрическое уравнение. Известно, что решением уравнения вида sinx=а является
$x = (-1)^n arcsin a + \pi n$
n ∈ Z
Подставляем в формулу
$x = (-1)^n arcsin \frac{1}{2} + \pi n$
По таблице смотрим, чему равен угол, синус которого 1/2 (или считаем на калькуляторе)
$arcsin \frac{1}{2} = \frac{ \pi }{6} \\ x = (-1)^n \frac{ \pi }{6} + \pi n$
Ответ:
$(-1)^n* \frac{ \pi }{6} + \pi n$
n ∈ Z

Answer 2

Solving the Equation 2sinx - 1 = 0

To solve the equation 2sinx - 1 = 0, we can isolate sinx by adding 1 to both sides and then dividing by 2. This gives us:

2sinx - 1 + 1 = 0 + 1 2sinx = 1 sinx = 1/2

Now, let's find the value of x for sinx = 1/2.

Finding the Value of sinx = 1/2

The value of x for sinx = 1/2 can be found using trigonometric principles. The angle whose sine is 1/2 is π/6 radians or 30 degrees. This is a well-known value in trigonometry.

Therefore, the solution to the equation sinx = 1/2 is: x = π/6 + 2πn or x = 30° + 360°n, where n is an integer.

This means that x can take on the value of π/6 plus any integer multiple of 2π, or 30 degrees plus any integer multiple of 360 degrees.

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