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What is [tex]\sin 30^{\circ}[/tex]?

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]


Sagot :

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].