Page 145 - How To Solve Word Problems In Calculus

dx dθ
Given: = 10 Find: when z = 300
dt dt
100
We could use the relationship tan θ = , but it will be easier
x
to deal with x if it appears in the numerator of the fraction.
We prefer the cotangent function.

x
cot θ =
100
x = 100 cot θ

It follows that

dx dθ
2
= 100(−csc θ)
dt dt
dx −100 dθ
= ·
2
dt sin θ dt
dθ
Solving for ,
dt
2
dθ −sin θ dx
= ·
dt 100 dt

1
From the diagram we can see that sin θ = when z = 300.
3
dθ 1/9
=− · 10
dt 100
1
=−
90
1
θ is decreasing at the rate of rad/sec.
90

EXAMPLE 3
A police car is 20 ft away from a long straight wall. Its bea-
con, rotating 1 revolution per second, shines a beam of light

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