To determine the value of [tex]\(\sin 30^{\circ}\)[/tex], let's review some fundamental trigonometric concepts related to angles and their sine values.
1. Understanding basic angles: In trigonometry, certain angles have well-known sine values. One of these angles is [tex]\(30^{\circ}\)[/tex].
2. Unit circle and sine values: On the unit circle, the sine of an angle represents the y-coordinate of the point where the terminal side of the angle intersects the circle. For [tex]\(30^{\circ}\)[/tex], this value is a well-known trigonometric ratio.
3. Standard trigonometric values: For an angle of [tex]\(30^{\circ}\)[/tex], its sine value is commonly known to be [tex]\(\frac{1}{2}\)[/tex]. This can also be illustrated by the properties of the special right triangle, specifically the 30-60-90 triangle.
Given the multiple-choice options:
A. 1
B. [tex]\(\sqrt{3}\)[/tex]
C. [tex]\(\frac{1}{\sqrt{2}}\)[/tex]
D. [tex]\(\frac{1}{\sqrt{3}}\)[/tex]
E. [tex]\(\frac{\sqrt{3}}{2}\)[/tex]
F. [tex]\(\frac{1}{2}\)[/tex]
The correct value of [tex]\(\sin 30^{\circ}\)[/tex] is:
[tex]\[ \frac{1}{2} \][/tex]
Therefore, the correct answer is:
F. [tex]\(\frac{1}{2}\)[/tex]
