Geometry
# Trigonometric Functions

\[ \Large \sin \left(30^\circ\right) = \ ? \]

\[ \huge \frac{\hspace{2mm} \frac{\hspace{2mm} \frac{\hspace{2mm} \frac{\hspace{2mm} \frac{\sin x}{\cos x}\hspace{2mm} }{\tan x}\hspace{2mm} }{\cot x}\hspace{2mm} }{\sec x}\hspace{2mm} }{\csc x}\]

Find the value of the above fraction tower if \(0^\circ < x < {90}^\circ\).

**True or False?**

\[ \sin ^{-1} \left( \sin \theta \right) = \theta. \]

The domain of \( \sin \theta \) is all real numbers.

Calculate

\[ \frac{ 9 \cot^2 60^\circ + \sec ^2 45 ^\circ - 4 \sin 90^\circ } { 3 \tan^2 30^\circ + \csc^2 45^\circ - \tan 45^\circ }. \]