To determine the value of [tex]\(\cos 60^\circ\)[/tex], let's break it down step-by-step:
1. First, we need to know what [tex]\(\cos 60^\circ\)[/tex] represents. Cosine is one of the primary trigonometric functions, which relates the angle of a right triangle to the ratio of the adjacent side to the hypotenuse.
2. The value of [tex]\(\cos 60^\circ\)[/tex] is a well-known trigonometric value. In fact, [tex]\(\cos 60^\circ\)[/tex] simplifies to [tex]\(\frac{1}{2}\)[/tex].
However, to confirm this, we could inspect the provided answers and match them to the expected cosine value:
- A. [tex]\(\frac{1}{2}\)[/tex]: Mathematically, [tex]\(\frac{1}{2}\)[/tex] is equivalent to 0.5.
- B. 2: This is a whole number and it does not correspond to the known trigonometric value for [tex]\(\cos 60^\circ\)[/tex].
- C. [tex]\(\frac{2}{\sqrt{3}}\)[/tex]: This equals approximately 1.1547 when calculated, which does not match [tex]\(\cos 60^\circ\)[/tex].
- D. [tex]\(\frac{\sqrt{3}}{2}\)[/tex]: This value equals approximately 0.8660, which again, does not match [tex]\(\cos 60^\circ\)[/tex].
When we compare these numbers to the known value of [tex]\(\cos 60^\circ\)[/tex], which is exactly 0.5, only the answer provided in Option A. [tex]\(\frac{1}{2}\)[/tex] matches.
Final Answer: A. [tex]\(\frac{1}{2}\)[/tex]
