Use identities to fill in each blank with the appropriate trigonometric function name.
tan 24° = 1/ _____ 66°

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Recall the complementary angle identity for tangent: \(\tan(\theta) = \cot(90^\circ - \theta)\), which means tangent of an angle is the cotangent of its complement.

Notice that \(24^\circ\) and \(66^\circ\) are complementary angles because \(24^\circ + 66^\circ = 90^\circ\).

Rewrite \(\tan 24^\circ\) using the complementary angle identity: \(\tan 24^\circ = \cot 66^\circ\).

Recall that cotangent is the reciprocal of tangent: \(\cot \alpha = \frac{1}{\tan \alpha}\).

Therefore, \(\tan 24^\circ = \frac{1}{\tan 66^\circ}\), so the blank should be filled with the function name 'tan'.

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