\( y=\sinh (1) \)

The given expression is \( y = \sinh(1) \). The hyperbolic sine function is defined as: \[ \sinh(x) = \frac{e^x - e^{-x}}{2} \] Substitute \( x = 1 \) into the expression: \[ y = \sinh(1) = \frac{e^1 - e^{-1}}{2} \] Now, we can calculate the value of \( y \) using the above expression. Calculate the value by following steps: - step0: Calculate: \(\frac{\left(e^{1}-e^{-1}\right)}{2}\) - step1: Remove the parentheses: \(\frac{e^{1}-e^{-1}}{2}\) - step2: Evaluate the power: \(\frac{e-e^{-1}}{2}\) - step3: Evaluate the power: \(\frac{\frac{e^{2}-1}{e}}{2}\) - step4: Multiply by the reciprocal: \(\frac{e^{2}-1}{e}\times \frac{1}{2}\) - step5: Multiply the fractions: \(\frac{e^{2}-1}{e\times 2}\) - step6: Multiply: \(\frac{e^{2}-1}{2e}\) The value of \( y = \sinh(1) \) is approximately 1.175201.