Answer :
To find the value of [tex]\(\sin 30^{\circ}\)[/tex], we follow a series of steps:
1. Understand that [tex]\(30^{\circ}\)[/tex] is an angle in a right-angled triangle:
- In a right-angled triangle with one of the angles being [tex]\(30^{\circ}\)[/tex], the sine function is defined as the ratio of the length of the opposite side to the hypotenuse.
2. Recall the exact values or use a calculator for basic trigonometric functions:
- The sine of [tex]\(30^{\circ}\)[/tex] is a well-known trigonometric identity that we often encounter in geometry and trigonometry.
3. Know the exact trigonometric value:
- The exact value of [tex]\(\sin 30^{\circ}\)[/tex] is known to be [tex]\(\frac{1}{2}\)[/tex].
Putting this all together, we conclude that:
[tex]\(\sin 30^{\circ} = \frac{1}{2}\)[/tex]
Given the options:
A. [tex]\(\frac{1}{\sqrt{3}}\)[/tex]
B. [tex]\(\frac{1}{\sqrt{2}}\)[/tex]
C. 1
D. [tex]\(\frac{\sqrt{3}}{2}\)[/tex]
E. [tex]\(\frac{1}{2}\)[/tex]
F. [tex]\(\sqrt{3}\)[/tex]
The correct answer is option E: [tex]\(\frac{1}{2}\)[/tex].
1. Understand that [tex]\(30^{\circ}\)[/tex] is an angle in a right-angled triangle:
- In a right-angled triangle with one of the angles being [tex]\(30^{\circ}\)[/tex], the sine function is defined as the ratio of the length of the opposite side to the hypotenuse.
2. Recall the exact values or use a calculator for basic trigonometric functions:
- The sine of [tex]\(30^{\circ}\)[/tex] is a well-known trigonometric identity that we often encounter in geometry and trigonometry.
3. Know the exact trigonometric value:
- The exact value of [tex]\(\sin 30^{\circ}\)[/tex] is known to be [tex]\(\frac{1}{2}\)[/tex].
Putting this all together, we conclude that:
[tex]\(\sin 30^{\circ} = \frac{1}{2}\)[/tex]
Given the options:
A. [tex]\(\frac{1}{\sqrt{3}}\)[/tex]
B. [tex]\(\frac{1}{\sqrt{2}}\)[/tex]
C. 1
D. [tex]\(\frac{\sqrt{3}}{2}\)[/tex]
E. [tex]\(\frac{1}{2}\)[/tex]
F. [tex]\(\sqrt{3}\)[/tex]
The correct answer is option E: [tex]\(\frac{1}{2}\)[/tex].
