Problem
Give the degree measure of $\theta$ if it exists. Do not use a calculator. \[ \theta=\cos ^{-1}(2) \] Select the correct choice below and fill in any answer boxes in your choice. A. $\theta=7^{\circ}$ (Type your answer in degrees.) B. $\cos ^{-1}(2)$ does not exist.
Solution
Step 1 ：Given that \(\theta=\cos^{-1}(2)\)
Step 2 ：The cosine function returns values between -1 and 1 for all real numbers.
Step 3 ：Therefore, \(\cos^{-1}(2)\) does not exist because 2 is outside the range of the cosine function.
Step 4 ：So, the final answer is \(\boxed{\cos^{-1}(2)\text{ does not exist}}\)
