Answer
a) $\sinh(1)\approx 1.1752$
b) $\sinh^{-1}(1)\approx 0.8814$
Work Step by Step
a) We know that:
$$\sinh(x)=\frac{e^{x}-e^{-x}}{2}$$
Substitute $x=1$ into the equation:
$$\sinh(1)=\frac{e^{1}-e^{-1}}{2}\approx 1.1752$$
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b) We know that:
$$\sinh^{-1}(x)=\ln(x+\sqrt{x^{2}+1})$$
Substitute $x=1$ into the equation:
$$\sinh^{-1}(1)=\ln(1+\sqrt{1^{2}+1})\approx 0.8814$$
