> See also: > - [[Notes/Trigonometry]] # Inverse Trigonometric Functions Only one-to-one functions can have an inverse. Review [[Domain and Range]] and functions to understand why. You must restrict the domain of certain trigonometric functions to find their inverse form. > If you use a calculator to graph an ivnerse trig function you will notice that its domain and range are limited. > - **Ex:** $sin^{-1}(x)$ ## Proofs of Inverse Trig Functions > [!check] Proving the Inverse of $sinh(x)$ > --- ## Solving Equations Using Inverse Trig Functions > [!help] Examples > $\begin{aligned} (\sqrt{3}) tan(x)+1=0 \\ (\sqrt{3}) tan(x)=-1 \\ tan(x)=-\frac{1}{\sqrt{3}}\\ x=tan^{-1}(-\frac{1}{\sqrt{3}}) \end{aligned}$ > --- > $\begin{aligned} 3sin(6x)=2 \\ sin(6x)=\frac{2}{3} \\ 6x=sin^{-1}(\frac{2}{3}) \\ x=\frac{sin^{-1}(\frac{2}{3})}{6} \end{aligned}$