Question

1)cos x/3 =- √2/2 2)sin(2x+П/4)= √3/2 3)2cos(x-П/6)= √3 4)tg(x+П/3)- √3=0

Answer 1

Ответ:

решение смотри на фотографии

Answer 2

To solve these trigonometric equations, you'll need to find the values of x that satisfy each equation. I'll provide the solutions step by step:

1. cos(x/3) = -√2/2 First, find the reference angle whose cosine is √2/2, which is π/4 radians. Since cos(x) = cos(-x), we can ignore the negative sign. So, x/3 = π/4.

   Now, solve for x: x = π/4 * 3 x = 3π/4

2. sin(2x + π/4) = √3/2 Find the reference angle whose sine is √3/2, which is π/3 radians. So, 2x + π/4 = π/3.

   Now, solve for x: 2x = π/3 - π/4 2x = (4π - 3π) / 12 2x = π / 12

   Divide by 2: x = π / 24

3. 2cos(x - π/6) = √3 First, divide both sides by 2: cos(x - π/6) = √3/2

   Find the reference angle whose cosine is √3/2, which is π/6 radians. So, x - π/6 = π/6.

   Now, solve for x: x = π/6 + π/6 x = 2π/6 x = π/3

4. tan(x + π/3) - √3 = 0 First, add √3 to both sides: tan(x + π/3) = √3

   Find the reference angle whose tangent is √3, which is π/3 radians. So, x + π/3 = π/3.

   Now, solve for x: x = π/3 - π/3 x = 0

So, the solutions to the equations are:

1. x = 3π/4
2. x = π/24
3. x = π/3
4. x = 0