Answer :
To rewrite [tex]\(\sin 15^\circ\)[/tex] in terms of the appropriate cofunction, we can use a property from trigonometry known as the cofunction identity. This identity states that:
[tex]\[ \sin(\theta) = \cos(90^\circ - \theta) \][/tex]
Here’s how you can apply this identity step-by-step:
1. Start with the given angle for the sine function, which is [tex]\(15^\circ\)[/tex].
2. Identify the cofunction identity for sine. According to the cofunction identity:
[tex]\[ \sin(\theta) = \cos(90^\circ - \theta) \][/tex]
3. Substitute [tex]\(\theta\)[/tex] with [tex]\(15^\circ\)[/tex] in the identity:
[tex]\[ \sin(15^\circ) = \cos(90^\circ - 15^\circ) \][/tex]
4. Perform the subtraction inside the cosine function:
[tex]\[ 90^\circ - 15^\circ = 75^\circ \][/tex]
Therefore,
[tex]\[ \sin(15^\circ) = \cos(75^\circ) \][/tex]
Thus, [tex]\(\sin 15^\circ\)[/tex] can be rewritten as [tex]\(\cos 75^\circ\)[/tex].
[tex]\[ \sin(\theta) = \cos(90^\circ - \theta) \][/tex]
Here’s how you can apply this identity step-by-step:
1. Start with the given angle for the sine function, which is [tex]\(15^\circ\)[/tex].
2. Identify the cofunction identity for sine. According to the cofunction identity:
[tex]\[ \sin(\theta) = \cos(90^\circ - \theta) \][/tex]
3. Substitute [tex]\(\theta\)[/tex] with [tex]\(15^\circ\)[/tex] in the identity:
[tex]\[ \sin(15^\circ) = \cos(90^\circ - 15^\circ) \][/tex]
4. Perform the subtraction inside the cosine function:
[tex]\[ 90^\circ - 15^\circ = 75^\circ \][/tex]
Therefore,
[tex]\[ \sin(15^\circ) = \cos(75^\circ) \][/tex]
Thus, [tex]\(\sin 15^\circ\)[/tex] can be rewritten as [tex]\(\cos 75^\circ\)[/tex].
