Page 142 - How To Solve Word Problems In Calculus

Chapter 5

Trigonometric Functions

In Chapters 3 and 4 we discussed techniques for solving re-
lated rates and maximum-minimum problems. These extend
directly to problems involving trigonometric functions. The
use of trigonometry can often simplify the solution of word
problems significantly.
The derivatives of the trigonometric functions play an
important role in the solution of these problems.

d d
sin x = cos x cos x =−sin x
dx dx
d 2 d 2
tan x = sec x cot x =−csc x
dx dx
d d
sec x = sec x tan x csc x =−csc x cot x
dx dx

It is important to remember that these derivative formulas are
correct only if x is expressed in radian measure. Therefore,
any angles or rates expressed in degrees should be converted
to radians. This can be easily accomplished by remembering
◦
that π radians is equivalent to 180 .
The Pythagorean identities are useful in simplifying
trigonometric expressions:

2
2
2
2
2
2
sin x + cos x = 1 tan x + 1 = sec x cot x + 1 = csc x
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