Decide whether the statement is possible or impossible.
\[
\cos \alpha=-\frac{1}{2} \text { and } \sec \alpha=2
\]
Is the statement possible or impossible?
Impossible
Possible

Answer

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Answer

Final Answer: The statement is \(\boxed{\text{impossible}}\).

Steps

Step 1 ：Decide whether the statement is possible or impossible: \(\cos \alpha=-\frac{1}{2}\) and \(\sec \alpha=2\)

Step 2 ：The secant of an angle is defined as the reciprocal of the cosine of the angle.

Step 3 ：So, if \(\cos(\alpha) = -\frac{1}{2}\), then \(\sec(\alpha)\) should be -2, not 2.

Step 4 ：Therefore, the statement is impossible.

Step 5 ：Final Answer: The statement is \(\boxed{\text{impossible}}\).