Question

Sin x=-1 как это решить ,тема урока: Определение синуса, косинуса, тангенса. Знаю только,что sin=y,cos=x, . За лучший ответ дам 20 баллов!!!!!

Answer 1

По таблице можно найти значение:
sin270=sin $\frac{3pi}{2}$=-1

Answer 2

Problem Analysis

To solve the equation sin(x) = -1, we need to find the value of x that satisfies this equation. We can use the properties of the sine function to determine the possible values of x.

Solution

The sine function (sin) is a periodic function that repeats itself every 2π radians or 360 degrees. The values of sin(x) range from -1 to 1. In this case, we are given that sin(x) = -1.

The value of sin(x) is -1 at two points in the unit circle: -π/2 and 3π/2. These are the angles where the terminal side of the angle intersects the unit circle at the point (-1, 0).

Therefore, the solutions to the equation sin(x) = -1 are x = -π/2 + 2πn and x = 3π/2 + 2πn, where n is an integer.

Let's find the values of x that satisfy the equation:

1. For x = -π/2 + 2πn: - When n = 0, x = -π/2. - When n = 1, x = 3π/2. - When n = 2, x = 7π/2. - ...

2. For x = 3π/2 + 2πn: - When n = 0, x = 3π/2. - When n = 1, x = 7π/2. - When n = 2, x = 11π/2. - ...

Therefore, the solutions to the equation sin(x) = -1 are x = -π/2 + 2πn and x = 3π/2 + 2πn, where n is an integer.

Answer

The solutions to the equation sin(x) = -1 are x = -π/2 + 2πn and x = 3π/2 + 2πn, where n is an integer. Some specific solutions include x = -π/2, x = 3π/2, x = 7π/2, x = 11π/2, and so on.

I hope this helps! Let me know if you have any further questions.