why 2x=cos inverse 1 (0)
equals to 2x= pi/2 or 3pi/2
The equation 2x = cos^(-1)(1) means finding the angle whose cosine is equal to 1.
The cosine function has a value of 1 at two specific angles: 0 radians (or 0 degrees) and 2π radians (or 360 degrees). These angles are the ones where the cosine function reaches its maximum value of 1.
When converting the equation to the range [0, 2π), it becomes:
2x = 0 or 2π
Dividing both sides by 2 gives:
x = 0 or x = π
So, in the interval [0, 2π), the equation 2x = cos^(-1)(1) is true when x is equal to 0 radians (or 0 degrees) or π radians (or 180 degrees).
However, the values π/2 and 3π/2 do not satisfy the equation 2x = cos^(-1)(1).
To solve the equation 2x = cos^(-1)(1), we need to find the values of x that satisfy this equation.
First, let's find the values of cos^(-1)(1). The cosine inverse function, cos^(-1)(x), gives the angle whose cosine is x.
In this case, we need to find the angle whose cosine is 1. The cosine of 1 is 1, so cos^(-1)(1) = 0.
Now let's substitute this value back into the original equation:
2x = 0
To solve for x, divide both sides of the equation by 2:
x = 0/2
Simplifying, we find that x = 0.
Therefore, the equation 2x = cos^(-1)(1) is true when x = 0.
So, the solution to the equation 2x = cos^(-1)(1) is x = 0.