To find which option is equivalent to \(\sin 51^\circ\), we can use the following trigonometric identities:
- \(\sin(90^\circ - x) = \cos x\)
- \(\tan x = \frac{\sin x}{\cos x}\)
Let's evaluate the options:
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A. \(\cos 51^\circ\): This is not equivalent to \(\sin 51^\circ\).
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B. \(\cos 39^\circ\): Since \(51^\circ + 39^\circ = 90^\circ\), we have \(\cos 39^\circ = \sin(90^\circ - 39^\circ) = \sin 51^\circ\). This one is equivalent!
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C. \(\tan 39^\circ\): This cannot be directly compared as \( \tan 39^\circ = \frac{\sin 39^\circ}{\cos 39^\circ} \) does not equal \(\sin 51^\circ\).
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D. \(\tan 51^\circ\): This again cannot be directly related to \(\sin 51^\circ\) in a way that would make them equivalent.
Thus, the equivalent expression to \(\sin 51^\circ\) is:
B. \(\cos 39^\circ\).