Question

question 8 of 10
which statement does not describe the cosine function?
a. the cycle repeats every 2π radians.
b. its range includes all real numbers.
c. the cycle starts at y = 1, decreases to y = -1, and then increases to y = 1.
d. its reciprocal function is secant.

Explanation:

To determine which statement does not describe the cosine function, we analyze each option:

• Option A: The cosine function has a period of \( 2\pi \) radians, meaning its cycle repeats every \( 2\pi \) radians. This is correct.
• Option B: The range of \( \cos(x) \) is \( [-1, 1] \), so it does not include all real numbers. This statement is incorrect.
• Option C: The cosine curve starts at \( (0, 1) \), decreases to \( (\pi, -1) \), then increases back to \( (2\pi, 1) \), matching the cycle described. This is correct.
• Option D: The reciprocal of \( \cos(x) \) is \( \sec(x) = \frac{1}{\cos(x)} \), so this is correct.

Answer:

B. Its range includes all real numbers.