To solve the equation sin(6x) * cos(6x) = -1/2, we can use the double angle formula for sine:
sin(2θ) = 2sin(θ)cos(θ)
Plugging in θ = 6x, we get:
sin(12x) = 2sin(6x)cos(6x)
Now we can rewrite the given equation using this double angle formula:
2sin(6x)cos(6x) = -1/2
Since sin(12x) = 2sin(6x)cos(6x), we can substitute sin(12x) into the equation:
sin(12x) = -1/2
To find the solutions for this equation, we need to determine where the sine function equals -1/2. This occurs at 30 degrees or pi/6 in radians.
Therefore, the solutions for x are:
12x = π/6 + 2nπ or 12x = 5π/6 + 2nπ, where n is an integer.
Solving for x, we get:
x = π/72 + nπ/6 or x = 5π/72 + nπ/6, where n is an integer.
To solve the equation sin(6x) * cos(6x) = -1/2, we can use the double angle formula for sine:
sin(2θ) = 2sin(θ)cos(θ)
Plugging in θ = 6x, we get:
sin(12x) = 2sin(6x)cos(6x)
Now we can rewrite the given equation using this double angle formula:
2sin(6x)cos(6x) = -1/2
Since sin(12x) = 2sin(6x)cos(6x), we can substitute sin(12x) into the equation:
sin(12x) = -1/2
To find the solutions for this equation, we need to determine where the sine function equals -1/2. This occurs at 30 degrees or pi/6 in radians.
Therefore, the solutions for x are:
12x = π/6 + 2nπ or 12x = 5π/6 + 2nπ, where n is an integer.
Solving for x, we get:
x = π/72 + nπ/6 or x = 5π/72 + nπ/6, where n is an integer.