To determine which of the given options is equivalent to [tex]\(\cos(23^\circ)\)[/tex], we can use trigonometric identities. One of the most useful identities in this context is the co-function identity, which relates the sine and cosine functions:
[tex]\[
\sin(90^\circ - \theta) = \cos(\theta)
\][/tex]
Here, [tex]\(\theta\)[/tex] is the angle we are considering. We want to find an equivalent expression for [tex]\(\cos(23^\circ)\)[/tex].
1. Using the co-function identity:
[tex]\[
\cos(23^\circ) = \sin(90^\circ - 23^\circ)
\][/tex]
2. Simplify the expression inside the sine function:
[tex]\[
\cos(23^\circ) = \sin(67^\circ)
\][/tex]
Therefore, [tex]\(\cos(23^\circ)\)[/tex] is equivalent to [tex]\(\sin(67^\circ)\)[/tex].
Now let's compare this with the given options:
- [tex]\(\sin(23^\circ)\)[/tex]
- [tex]\(\cos(67^\circ)\)[/tex]
- [tex]\(\sin(67^\circ)\)[/tex]
- [tex]\(\cos(90^\circ)\)[/tex]
From our step-by-step solution:
[tex]\[
\cos(23^\circ) = \sin(67^\circ)
\][/tex]
Hence, the correct answer is:
[tex]\[
\sin(67^\circ)
\][/tex]
