Using cofunctions of complementary angles, which expression is equivalent to $\sin 51°$?

• A. $\tan 39°$
• B. $\cos 39°$
• C. $\sin 39°$
• D. $\cos 51°$

Answer: (B)

Verified step by step guidance

1. Recall the cofunction identity for sine and cosine: for any angle \( \theta \), \( \sin(\theta) = \cos(90^\circ - \theta) \). This means sine of an angle is equal to cosine of its complement.
2. Identify the complementary angle of \( 51^\circ \) by subtracting it from \( 90^\circ \): \( 90^\circ - 51^\circ = 39^\circ \).
3. Apply the cofunction identity to rewrite \( \sin(51^\circ) \) as \( \cos(39^\circ) \) using the formula from step 1.
4. Compare the expression \( \cos(39^\circ) \) with the given options to find the equivalent expression to \( \sin(51^\circ) \).
5. Note that the other options \( \tan(39^\circ) \), \( \sin(39^\circ) \), and \( \cos(51^\circ) \) do not represent the cofunction equivalent of \( \sin(51^\circ) \).