Question

4sin x = -2^3 Тригонаметрическое уравнение

Answer 1

$4sin x = -2^3 \\ sinx = - \frac{8}{4} \\ sinx = - 2$
но синус - ограниченная функция
$| \: sinx \: | \leqslant 1$
поэтому
x∈∅

решений нет

Answer 2

To solve the trigonometric equation 4sin(x) = -2^3, we need to find the values of x that satisfy the equation. Let's break it down step-by-step:

Step 1: Simplify the equation. -2^3 means -2 raised to the power of 3, which is equal to -8. Therefore, the equation becomes: 4sin(x) = -8

Step 2: Isolate sin(x) by dividing both sides by 4: sin(x) = -8/4 sin(x) = -2

However, there's a problem here. The sine function ranges from -1 to 1, and there is no real value of x that will make sin(x) equal to -2. Therefore, this equation has no solution in real numbers.

If you are considering complex solutions, you can use the inverse sine function (also called arcsine) to find complex values of x. The solution would be:

x = arcsin(-2) + 2πk or x = π - arcsin(-2) + 2πk

where k is an integer, and arcsin denotes the inverse sine function. Note that these solutions will be complex numbers.

Keep in mind that the standard convention for the arcsine function provides results in the range of -π/2 to π/2 (or -90° to 90°). Therefore, the solutions above are general solutions, and you may need to restrict them based on the specific range of x you are interested in.