Applications of Trigonometric Functions

1
Applications of Trigonometric Functions

• Section 4.8

2
Objectives

• Model simple harmonic motion
• Determine the maximum displacement, frequency,
  and period of an object in simple harmonic motion
• Apply Law of Sines and Law of Cosine to solve
  triangles.

3
Vocabulary

• simple harmonic motion up and down oscillations
  (ignoring friction and resistance)
• equilibrium position rest position
• maximum displacement - amplitude
• period how long it takes for the motion to go
  through one complete cycle
• frequency one divided by the period

4
Formulas

• simple harmonic motion

used when the object is at its greatest distance
from rest position at the origin
used when the object is at its rest position at
the origin
5
An object is attached to a coiled spring. The
object is pulled down 6 centimeters from the rest
position and then released. The period of the
motion is 4 seconds. Write an equation for the
distance of the object from its rest position t
seconds.
6
An object is attached to a coiled spring. The
object is initially at rest position and then
pulled down 5 centimeters from the rest position
and then released. The period of the motion is
1.5 seconds. Write an equation for the distance
of the object from its rest position t seconds.
7
An object in simple harmonic motion is described
by the equation below, where t is measured in
seconds and d is in inches.

• Find each of the following
• The maximum displacement
• The frequency
• The time required for one cycle

8

• Solve the triangle

C
a 10
b 12
A
B
c 16
9
Determine if the following measurements produce
one triangle, two triangles, or no triangles.
a 10, b 40, A 60?
10
Determine if the following measurements produce
one triangle, two triangles, or no triangles.
a 42.1, b 37, A 112?
11
Determine if the following measurements produce
one triangle, two triangles, or no triangles.
a 20, b 15, A 40?