Question

simplify the expression.
\frac{1 - \cos 52.74^{\circ}}{\sin 52.74^{\circ}}
\frac{1 - \cos 52.74^{\circ}}{\sin 52.74^{\circ}} = \square^{\circ}
(simplify your answer. use integers or decimals for any numbers in the expression

Explanation:

Step1: Use the half - angle formula

We know that \(\tan\frac{\alpha}{2}=\frac{1 - \cos\alpha}{\sin\alpha}\). Let \(\alpha = 52.74^{\circ}\), then the given expression \(\frac{1-\cos52.74^{\circ}}{\sin52.74^{\circ}}\) is in the form of the half - angle formula for tangent.

Step2: Calculate \(\frac{\alpha}{2}\)

Substitute \(\alpha = 52.74^{\circ}\) into \(\frac{\alpha}{2}\). We get \(\frac{52.74^{\circ}}{2}=26.37^{\circ}\)

Answer:

\(26.37\)