Decide whether the statement is possible or impossible. \[ \sec \theta=4 \] Is the statement possible or impossible? Impossible Possible

Step 1 ：Decide whether the statement is possible or impossible.

Step 2 ：\[\sec \theta=4\]

Step 3 ：Is the statement possible or impossible?

Step 4 ：The secant of an angle in a right triangle is defined as the ratio of the hypotenuse to the adjacent side. The secant function is the reciprocal of the cosine function. The range of the cosine function is -1 to 1, so the range of the secant function is from negative infinity to -1 and from 1 to positive infinity. Therefore, it is possible for sec θ to be 4.

Step 5 ：The Python code checks for all angles from 0 to 360 degrees if the secant of the angle is approximately 4. The result is False, which means that there is no such angle in this range for which the secant is 4. However, this does not mean that it is impossible for sec θ to be 4. The secant function is not limited to values between -1 and 1 like the cosine function. It can take any value except 0. Therefore, it is possible for sec θ to be 4.

Step 6 ：Final Answer: \(\boxed{\text{Possible}}\)