Question

Решите уравнение 0,5+sin(3П/2+x)=0. В ответ запишите величину наименьшего положительного корня уравнения,выраженную в градусах Помогите пожалуйста,очень нужно!!!!

Answer 1

 0,5 - cosx =0;   cosx = 1/2; $x = 60^{0}$

Answer 2

Solving the Equation

To solve the equation 0.5 sin(3π/2 + x) = 0, we can follow these steps:

Step 1: Rewrite the equation using the trigonometric identity sin(a + b) = sin(a)cos(b) + cos(a)sin(b): 0.5(sin(3π/2)cos(x) + cos(3π/2)sin(x)) = 0

Step 2: Simplify the equation using the values of sin(3π/2) and cos(3π/2): 0.5(0 * cos(x) + (-1) * sin(x)) = 0

Step 3: Simplify further: -0.5sin(x) = 0

Step 4: Divide both sides of the equation by -0.5 to isolate sin(x): sin(x) = 0

Finding the Smallest Positive Root in Degrees

To find the smallest positive root of the equation sin(x) = 0 expressed in degrees, we need to determine the values of x that satisfy this equation.

The sine function has a period of 360 degrees, which means it repeats every 360 degrees. The solutions to the equation sin(x) = 0 occur when x is an integer multiple of 180 degrees.

The smallest positive root of the equation is when x = 0 degrees. This is because the sine function is equal to 0 at x = 0, and it is the smallest positive value that satisfies the equation.

Therefore, the smallest positive root of the equation sin(x) = 0 expressed in degrees is 0 degrees.

Please note that the sources provided did not contain specific information related to this equation. The solution was derived based on mathematical principles and knowledge of trigonometric functions.