Question

(a) To determine the numerical value of given expression.

(b) To determine the numerical value of given expression.

Short answer

(a) The numerical value of \(\sinh 0\) is 0.

(b) The numerical value of \(\cos h0\) is 1.

Step-by-step solution

Given expressions

(a)The expression is \(\sinh 0\).

(b)The expression is \(\cos h0\).

Concept of hyperbolic function

The Definition of hyperbolic function:

\(\begin{array}{l}sinhx = \frac{{{e^x} - {e^{ - x}}}}{2}\\coshx = \frac{{{e^x} + {e^{ - x}}}}{2}\end{array}\)

Use formula and substitute the values

(b)

Obtain the value of the expression \(\cos h0\).

Use definition of the hyperbolic function \(\cos h0 = \frac{{{e^2} + {e^{ - x}}}}{2}\).

Substitute 0 for \(x\).

\(\begin{array}{c}\cos h0 = \frac{{{e^\theta } + {e^\theta }}}{2}\\ = \frac{{1 + 1}}{2}\\ = 1\end{array}\)

Thus, the value of \(\cos h0 = 1\).