-sinx-cosx = 0
x=?
please and thank you! i'd appreciate it!
divide both sides by -cosx
tanx+1=0
x= arctan -1
x=-45 deg
To solve the equation -sin(x) - cos(x) = 0, we need to find the values of x that satisfy the equation.
Step 1: Rearrange the equation
Start by adding sin(x) to both sides: -sin(x) - cos(x) + sin(x) = sin(x)
Simplify the equation: -cos(x) = sin(x)
Step 2: Use the Pythagorean identity
The Pythagorean identity states that sin²(x) + cos²(x) = 1. Rearrange this equation to solve for sin(x) or cos(x):
cos²(x) = 1 - sin²(x) or sin²(x) = 1 - cos²(x).
Step 3: Substitute into the equation
Substitute the expression for sin(x) obtained from the Pythagorean identity into the equation -cos(x) = sin(x):
-cos(x) = √(1 - cos²(x))
Step 4: Solve for cos(x)
Square both sides of the equation:
(-cos(x))² = (√(1 - cos²(x)))²
cos²(x) = 1 - cos²(x)
2cos²(x) = 1
cos²(x) = 1/2
Step 5: Solve for cos(x)
Take the square root of both sides:
cos(x) = ±√(1/2)
Step 6: Find the values of x
To find the values of x, we need to determine when cosine is equal to ±√(1/2). Using a calculator or trigonometric table, we find that:
cos(x) = √(1/2) when x = π/4 + 2πn, where n is an integer.
cos(x) = -√(1/2) when x = 3π/4 + 2πn, where n is an integer.
Therefore, x can take on the values:
x = π/4 + 2πn or x = 3π/4 + 2πn, where n is an integer.
In summary, the solutions to the equation -sin(x) - cos(x) = 0 are x = π/4 + 2πn or x = 3π/4 + 2πn, where n is an integer.