Answer :
To determine the value of [tex]\(\cos 60^{\circ}\)[/tex], we can refer to the fundamental principles of trigonometry. The cosine function is part of the trigonometric functions and is extensively used in geometry, especially when dealing with right triangles and the unit circle.
In the context of the unit circle:
- The unit circle is a circle with a radius of 1 centered at the origin of a coordinate plane.
- The angle in trigonometry, like [tex]\(60^{\circ}\)[/tex], can be understood through this circle.
- The cosine of an angle is defined based on the x-coordinate of the point on the unit circle.
Now focusing on the specific angle:
- For [tex]\(60^{\circ}\)[/tex], it is a well-known standard angle commonly used in trigonometry.
- Cosine of standard angles including [tex]\(0^{\circ}\)[/tex], [tex]\(30^{\circ}\)[/tex], [tex]\(45^{\circ}\)[/tex], [tex]\(60^{\circ}\)[/tex], and [tex]\(90^{\circ}\)[/tex] are typically memorized because of their frequent application.
For the angle [tex]\(60^{\circ}\)[/tex]:
- The cosine of [tex]\(60^{\circ}\)[/tex] is equal to [tex]\(\frac{1}{2}\)[/tex].
Thus, the value of [tex]\(\cos 60^{\circ}\)[/tex] is [tex]\(\frac{1}{2}\)[/tex].
Therefore, the correct answer is:
B. [tex]\(\frac{1}{2}\)[/tex]
In the context of the unit circle:
- The unit circle is a circle with a radius of 1 centered at the origin of a coordinate plane.
- The angle in trigonometry, like [tex]\(60^{\circ}\)[/tex], can be understood through this circle.
- The cosine of an angle is defined based on the x-coordinate of the point on the unit circle.
Now focusing on the specific angle:
- For [tex]\(60^{\circ}\)[/tex], it is a well-known standard angle commonly used in trigonometry.
- Cosine of standard angles including [tex]\(0^{\circ}\)[/tex], [tex]\(30^{\circ}\)[/tex], [tex]\(45^{\circ}\)[/tex], [tex]\(60^{\circ}\)[/tex], and [tex]\(90^{\circ}\)[/tex] are typically memorized because of their frequent application.
For the angle [tex]\(60^{\circ}\)[/tex]:
- The cosine of [tex]\(60^{\circ}\)[/tex] is equal to [tex]\(\frac{1}{2}\)[/tex].
Thus, the value of [tex]\(\cos 60^{\circ}\)[/tex] is [tex]\(\frac{1}{2}\)[/tex].
Therefore, the correct answer is:
B. [tex]\(\frac{1}{2}\)[/tex]
