Page 156 - How To Solve Word Problems In Calculus

dx dθ
Given: = 2 Find: when x = 6
dt dt

x
= sin θ
10
x = 10 sin θ

dx dθ
= 10 cos θ
dt dt

At the instant in question, x = 6. By the theorem of Pythagoras,
8
y = 8. It follows that cos θ = .
10
8 dθ
2 = 10 · ·
10 dt

dθ
2 = 8
dt
dθ 1
=
dt 4

1
The angle is increasing at the rate of radian per minute.
4
2.

3
θ
4
2 per second is equivalent to π/90 radians per second.
◦
45 = π/4 radians.
◦
dθ π dA
Given: = Find: when θ = π/4
dt 90 dt
The area of a triangle with sides a and b and included angle θ
1
is ab sin θ. Since a = 3 and b = 4, this reduces to A = 6 sin θ.
2

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