Answer :
Given the problem of finding the exact value of [tex]\(\cos(-60^\circ)\)[/tex], we will start by applying some properties of trigonometric functions.
1. Cosine of an Angle's Property:
Cosine is an even function, which means that [tex]\(\cos(-\theta) = \cos(\theta)\)[/tex]. This property will simplify our problem since it allows us to remove the negative sign from the angle:
[tex]\[ \cos(-60^\circ) = \cos(60^\circ) \][/tex]
2. Cosine of 60 Degrees:
Next, we need to determine the cosine of 60 degrees. This is a well-known value in trigonometry. The cosine of 60 degrees is:
[tex]\[ \cos(60^\circ) = \frac{1}{2} \][/tex]
Thus, combining these steps, we find:
[tex]\[ \cos(-60^\circ) = \cos(60^\circ) = \frac{1}{2} \][/tex]
Therefore, among the given options:
- [tex]\(-\frac{\sqrt{3}}{2}\)[/tex]
- [tex]\(-\frac{1}{2}\)[/tex]
- [tex]\(\frac{1}{2}\)[/tex]
- [tex]\(\frac{\sqrt{3}}{2}\)[/tex]
The exact value of [tex]\(\cos(-60^\circ)\)[/tex] is [tex]\(\frac{1}{2}\)[/tex].
Hence, the correct answer is [tex]\(\boxed{3}\)[/tex].
1. Cosine of an Angle's Property:
Cosine is an even function, which means that [tex]\(\cos(-\theta) = \cos(\theta)\)[/tex]. This property will simplify our problem since it allows us to remove the negative sign from the angle:
[tex]\[ \cos(-60^\circ) = \cos(60^\circ) \][/tex]
2. Cosine of 60 Degrees:
Next, we need to determine the cosine of 60 degrees. This is a well-known value in trigonometry. The cosine of 60 degrees is:
[tex]\[ \cos(60^\circ) = \frac{1}{2} \][/tex]
Thus, combining these steps, we find:
[tex]\[ \cos(-60^\circ) = \cos(60^\circ) = \frac{1}{2} \][/tex]
Therefore, among the given options:
- [tex]\(-\frac{\sqrt{3}}{2}\)[/tex]
- [tex]\(-\frac{1}{2}\)[/tex]
- [tex]\(\frac{1}{2}\)[/tex]
- [tex]\(\frac{\sqrt{3}}{2}\)[/tex]
The exact value of [tex]\(\cos(-60^\circ)\)[/tex] is [tex]\(\frac{1}{2}\)[/tex].
Hence, the correct answer is [tex]\(\boxed{3}\)[/tex].
