Question

ребяты, помогайте:)модуль синуса х = косинус хкак такое решать?спасибо)

Answer 1

Разделим обе части уравнения на cosx

тогда получим
tgx +1=0 

tgx = -1

отсюда х= -pi/4 +pi*n,где n принадлежит Z

Answer 2

Solving the Equation: Module of Sine x = Cosine x

To solve the equation |sin(x)| = cos(x), we can approach it by considering different cases based on the values of x. Let's break it down step by step:

1. Case 1: x is in the range [0, π/2] - In this case, both sin(x) and cos(x) are positive. - The equation becomes sin(x) = cos(x). - We can solve this equation by taking the arctangent of both sides: x = arctan(1) = π/4.

2. Case 2: x is in the range [π/2, π] - In this case, sin(x) is positive and cos(x) is negative. - The equation becomes sin(x) = -cos(x). - We can solve this equation by taking the arctangent of both sides: x = arctan(-1) = 3π/4.

3. Case 3: x is in the range [π, 3π/2] - In this case, both sin(x) and cos(x) are negative. - The equation becomes -sin(x) = -cos(x). - We can solve this equation by taking the arctangent of both sides: x = arctan(1) + π = 5π/4.

4. Case 4: x is in the range [3π/2, 2π] - In this case, sin(x) is negative and cos(x) is positive. - The equation becomes -sin(x) = cos(x). - We can solve this equation by taking the arctangent of both sides: x = arctan(-1) + π = 7π/4.

Therefore, the solutions to the equation |sin(x)| = cos(x) are: - x = π/4 - x = 3π/4 - x = 5π/4 - x = 7π/4

Please note that these solutions are valid for the given range of x values. If the range of x is different, the solutions may vary.

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