Homework Solutions, Section 7.6

Exercise 8:

We want to show that cosh(x) is an even function.

cosh(x)=[Graphics:7.6.probsgr1.gif]
cosh(-x)=[Graphics:7.6.probsgr2.gif]=[Graphics:7.6.probsgr3.gif]=cosh(x)
QED

Exercise 49:

[Graphics:7.6.probsgr5.gif][Graphics:7.6.probsgr4.gif]
[Graphics:7.6.probsgr5.gif][Graphics:7.6.probsgr6.gif]

h is the derivative of f:

[Graphics:7.6.probsgr5.gif][Graphics:7.6.probsgr7.gif]
[Graphics:7.6.probsgr5.gif][Graphics:7.6.probsgr8.gif]

We evaluate the derivative at 7 to get the slope:

[Graphics:7.6.probsgr5.gif][Graphics:7.6.probsgr9.gif]
[Graphics:7.6.probsgr5.gif][Graphics:7.6.probsgr10.gif]

The Cotangent of the angle theta is the rise over run, or the slope: so the ArcCot of the slope gives the angle:

[Graphics:7.6.probsgr5.gif][Graphics:7.6.probsgr11.gif]
[Graphics:7.6.probsgr5.gif][Graphics:7.6.probsgr12.gif]