Need help with Cosh calculations? below is the problem I think I have sussed question a) but I'm well stuck

Question

I've tried question B & transposed the formula but then get syntax error when using the calculator

A chain hangs so that its shape is of the form:

Y=48cosh(a/48)

Determine, correct to four significant figures, using the definition
Cosh(x)=e^x + e^-x/2
a) Find the value of y when a = 25.
b) Find the value of a when y = 60.

Answer 1

a)

y = 48cosh(25/48) = 48(e^(25/48) + e^(-25/48))/2 = 54.66

b)

60 = 48(e^(a/48) + e^(-a/48))/2 = 24(e^(a/48) + e^(-a/48)
60/24 = 5/2 = e^(a/48) + e^(-a/48)

Let u = e^(a/48).

Then u^(-1) = e^(-a/48)

5/2 = u + u^(-1)

Multiplying through by u:

5/2u = u² + 1
0 = u² - 5/2u + 1
0 = 2u² - 5u + 2
0 = (u - 2)(2u - 1)

If u = 2, then

e^(a/48) = 2
a/48 = ln(2)
a = 48ln(2) = 33.27

If u = 1/2, then

e^(a/48) = 1/2
a/48 = ln(1/2)
a = 48ln(1/2) = -33.27