what is the range of a cosine function?\na. irrational numbers\nc. positive numbers\nb. negative numbers\nd…

Brief Explanations:

The range of a function is the set of all possible output values. For the cosine function (y = \cos(x)), the maximum value is (1) (when (x = 2k\pi,k\in\mathbb{Z})) and the minimum value is (- 1) (when (x=(2k + 1)\pi,k\in\mathbb{Z})). Since the cosine function is continuous, it takes on all values between (-1) and (1).

• Option a: Irrational numbers are not relevant as the range of cosine is about bounded real - valued intervals, not the type of number (rational vs. irrational).
• Option b: The cosine function can take non - negative values (e.g., (\cos(0)=1), (\cos(\frac{\pi}{2}) = 0)).
• Option c: The cosine function can take non - positive values (e.g., (\cos(\pi)=-1), (\cos(\frac{3\pi}{2}) = 0)).
• Option d: Matches the property that (-1\leqslant\cos(x)\leqslant1) for all (x\in\mathbb{R}).

Answer:

D. All real numbers between -1 and 1 including -1 and 1