Students will learn how to simplify expressions of the form \(g(f(x)),\) where \(x\) is some angle, \(f\) is one of the inverse trig functions, and \(g\) is one of the six basic trig functions. For example, simplify \(\cos\left(\sin^{-1} 2x\right).\) Students will also learn how to find the domain and range for functions \(h(x) = g(f(x)).\) For example, what is the domain and range of \(f(x) = \sin\left(\tan^{-1} x\right)?\)