Page 148 - How To Solve Word Problems In Calculus

1
When the runner has run of the way around the track,
4
θ = π/2. Triangle ORT then becomes a right triangle.

2
2
x = 100 + 100 2 s = r θ
= 20,000 s = 100 θ
√ ds dθ
x = 100 2 = 100
dt dt

dθ
10 = 100
dt
dθ 1
=
dt 10
dx
We can now compute :
dt
dx dθ
x = 10,000 sin θ
dt dt
1

√ dx π 1
100 2 = 10,000 · sin ·
dt 2 10
√ dx
100 2 = 1000
dt
dx 1000 10 √
= √ = √ = 5 2 m/sec
dt 100 2 2

Maximum-Minimum Problems
Many maximum-minimum problems are conveniently solved
by introducing trigonometric functions.

EXAMPLE 5
What is the largest possible area of a triangle, two of whose
sides are a and b?

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