To find the value of [tex]\(\sin 30^\circ\)[/tex], let’s follow these steps:
1. Angle Conversion:
We start by understanding that [tex]\(\sin\)[/tex] function works with angles. In trigonometry, the sine of an angle is a fundamental concept that relates the angle to the ratio of the lengths of sides in a right triangle.
2. Recognize Known Values:
There are standard angles for which the sine, cosine, and tangent values are commonly known and should be memorized. One such standard angle is [tex]\(30^\circ\)[/tex].
3. Sine of 30 Degrees:
The sine of 30 degrees is a well-known trigonometric value. It is derived from the properties of a 30-60-90 triangle, which is a special right triangle. In such a triangle, the side opposite the 30-degree angle is half the length of the hypotenuse.
4. Exact Value:
The exact value of [tex]\(\sin 30^\circ\)[/tex] is [tex]\(\frac{1}{2}\)[/tex]. This is because, in a 30-60-90 triangle, if the hypotenuse is 1, the side opposite the 30-degree angle is [tex]\( \frac{1}{2} \)[/tex].
5. Given Choices:
Considering the multiple-choice options provided:
- A. [tex]\(\frac{\sqrt{3}}{2}\)[/tex]
- B. 1
The correct answer is neither of the options provided. The exact value of [tex]\(\sin 30^\circ\)[/tex] is [tex]\(\frac{1}{2}\)[/tex], which approximates to 0.5.
To recapitulate, [tex]\(\sin 30^\circ = 0.5\)[/tex], but none of the provided choices match this correct value. It seems there is an error in the provided choices as neither accurately reflects the true value of [tex]\(\sin 30^\circ\)[/tex].
