Since sin(30°) = 1/2 and sin(150°) = -1/2, we know that the angle within the sine function should be equivalent to either 30° or 150°. Therefore, solve for 3x + 2:
3x + 2 = 150 3x = 150° - 3x = 148 x = 148° / x ≈ 49.33°
or
3x + 2 = 30 3x = 30° - 3x = 28 x = 28° / x ≈ 9.33°
So, x ≈ 49.33° or x ≈ 9.33°
Move on to the second equation 2 ctg(П:3 - х) = 1 : √3
First, find the value inside the cotangent function:
П:3 - х = 60° - x
Now, find the cotangent of 60°:
ctg(60°) = 1/√3
So, solve for x:
2(1/√3) = 1/√ x = 60°
Therefore, the solution to the second equation is x = 60°
In conclusion, the solutions to the equations are x ≈ 49.33°, x ≈ 9.33°, and x = 60°.
To solve the equations:
Start with the first equationSin(3x + 2) = - √3
Since sin(30°) = 1/2 and sin(150°) = -1/2, we know that the angle within the sine function should be equivalent to either 30° or 150°. Therefore, solve for 3x + 2:
3x + 2 = 150
3x = 150° -
3x = 148
x = 148° /
x ≈ 49.33°
or
3x + 2 = 30
3x = 30° -
3x = 28
x = 28° /
x ≈ 9.33°
So, x ≈ 49.33° or x ≈ 9.33°
Move on to the second equation2 ctg(П:3 - х) = 1 : √3
First, find the value inside the cotangent function:
П:3 - х = 60° - x
Now, find the cotangent of 60°:
ctg(60°) = 1/√3
So, solve for x:
2(1/√3) = 1/√
x = 60°
Therefore, the solution to the second equation is x = 60°
In conclusion, the solutions to the equations are x ≈ 49.33°, x ≈ 9.33°, and x = 60°.