Question: (\[ \cos x = t \]\)…

\(\[ \cos x = t \]\)

Solution

Step 1 Given the equation: \[ \cos x = t & \] Step 2 Take the inverse cosine of both sides to solve for \( x \): \[ x = \cos^{-1} t & \] Step 3 Considering the periodicity of the cosine function, the general solution is: \[ x = \cos^{-1} t + 2\pi n \\ x = -\cos^{-1} t + 2\pi n & \] where \( n \) is any integer.