Inverse Cosine C8A63A

1. The problem is to find the inverse of the function \( \cos(\theta) = \frac{1}{3} \).\n\n2. The inverse cosine function, denoted as \( \cos^{-1}(x) \) or \( \arccos(x) \), gives the angle \( \theta \) whose cosine is \( x \).\n\n3. To find \( \theta \), use the formula:\n$$\theta = \cos^{-1}\left(\frac{1}{3}\right)$$\n\n4. Important note: The cosine function is only invertible on the interval \( [0, \pi] \), so the inverse cosine will return an angle in this range.\n\n5. Calculate the value using a calculator or tables:\n$$\theta \approx \cos^{-1}(0.3333) \approx 1.23096 \text{ radians}$$\n\n6. If you cannot get the inverse, it might be due to calculator mode (degrees vs radians) or input error. Make sure your calculator is set to the correct mode and you input the value correctly.\n\n7. Final answer:\n$$\theta \approx 1.231 \text{ radians}$$