Transcript Basic Functions and Their Graphs

Applications of
Trigonometric Functions
Section 4.8
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.
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
Formulas
• simple harmonic motion
d  a cost 
used when the object is
at its greatest distance
from rest position at
the origin
d  a sint 
used when the object is
at its rest position at
the origin
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 it’s
rest position t seconds.
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
it’s rest position t seconds.
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
 

d  5 cos  t 
2 
 3 
d  4 sin  t 
 2 
• The maximum displacement
• The frequency
• The time required for one
cycle
Solve the triangle
C
a = 10
b = 12
A
c = 16
B
Determine if the following
measurements produce one
triangle, two triangles, or no
triangles.
a = 10, b = 40, A = 60
Determine if the following
measurements produce one
triangle, two triangles, or no
triangles.
a = 42.1, b = 37, A = 112
Determine if the following
measurements produce one
triangle, two triangles, or no
triangles.
a = 20, b = 15, A = 40