Chapter 10 Trigonometric functions - Ugrad.math.ubc.ca

Math 102 Notes Chapter 10
θ
1
θ
2
x
Figure 10.12:
dθ 2
dt = −2π radians per hour.
12
The angle between the two hands is the difference of the two angles, i.e.
θ = θ 1 − θ 2
Thus,
dθ
dt = d dt (θ 1 − θ 2 ) = dθ 1
dt − dθ 2 2π
= −2π +
dt 12
Thus, we find that the rate of change of the angle between the hands is
dθ
dt = −2π11 12 = −π11 6 .
θ −θ
1
2
x
Figure 10.13:
Solution to (b):
We use the law of cosines to give us the rate of change of the desired distance. We have the triangle
shown in figure 10.12 in which side lengths are a = 3, b = 4, and c(t) opposite the angle θ(t). From
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