Chapter 2: Differentiation

Section 2.8: The Inverse Trig Functions and Their Derivatives

Example 2.8.2

$$ Graph the inverse of $\arcsin \left(x\right)$ by graphing parametrically the points $\left(\arcsin \left(x\right)\,x\right)$. $$ Solution $$ Graphing parametrically with the Plot Builder •  Type the list $\left[\arcsin \left(x\right)\,x\right]$   •  Context Panel: Plot Builder≻2-D plot (parametric) In Global Options, scaling≻constrained   •  The curve drawn is the principal branch of the sine function, drawn on the domain $\left[-\mathrm{\π}\/2\,\mathrm{\π}\/2\right]$. The inverse of arcsine is the sine, but only the principal branch of the sine function, the part used for defining the arcsine function.   $\left[\arcsin \left(x\right)\,x\right]$$\to$ Graphing parametrically with the plot command (To execute the command, select Evaluate in the Context Panel.) $\mathrm{plot}\left(\left[\arcsin \left(x\right)\,x\,x\=-3..3\right]\right)$ $$

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