Question

Sin x cos y = -0,5,sin y cos x = 0,5;​

Answer 1

Ответ:

У₁= п/6+2пк ;  Х=2пк

У₂=5п/6 +2пк  ;

Объяснение:

sin x cos y = -0,5,

sin y cos x = 0,5;​ почленно делим первое на второе.

Слева получаем

sin x cos y       =  -1  

sin y cos x

тангенс Х*котангенс У=-1

tg X*ctg Y=-1

tg X=-1/ctg Y= - tg Y=-sin Y/cos Y

подставляем в первое

-sin Y/cos Y *cos y = -0,5; косинус сокращается

sin Y = 0,5;   0,5 cos x = 0,5;​     cos x = 1 ; Х=2пк

У= п/6+2пк ;  Х=2пк

или У=5п/6 +2пк  ; Х=2пк

Answer 2

To solve the given equations:

Equation 1: sin(x) cos(y) = -0.5 Equation 2: sin(y) cos(x) = 0.5

We can use the trigonometric identity sin(2θ) = 2sin(θ)cos(θ) to simplify the equations.

Let's multiply Equation 1 by 2:

2sin(x) cos(y) = -1

Now, let's subtract Equation 2 from this new equation:

2sin(x) cos(y) - sin(y) cos(x) = -1 - 0.5 2sin(x) cos(y) - sin(y) cos(x) = -1.5

We can rewrite this equation using the trigonometric identity:

sin(x + y) = -1.5

However, there is no solution for sin(x + y) = -1.5 because the range of the sine function is [-1, 1]. Therefore, there are no values of x and y that satisfy both equations simultaneously.