angle of elevation the angle of elevation is measured from a horizontal line looking up at something
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Angle of Elevatio
n
The angle of elevation is measured from a horizontal line looking up at something.
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The Angle of Depression is measured from a horizontal line looking down at something.
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An outdoor basketball backboard casts a shadow 17 1/3 feet long. The angle of elevation from a point at the end of the shadow to the top of the backboard is 35.8°. Find the height of the backboard.
What would you want to do first? Draw a picture!
17 1/3 ftshadow
h
35.8°
Now you see that this is nothing but a right triangle trig problem. What trig function would you use that relates the angle and side you know to the side you want to know?
31
178.35tan
h
h8.35tan3
117
ft 5.12h
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Many physical phenomena can be modeled with simple harmonic motion.
the swinging of a pendulum
radio and television waves
light and sound waves water waves
a spring-mass system
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An object that moves on a coordinate
axis so that its distance from its rest
position at time is
simple harm
given by either
cos or sin
where and 0 are constants,
moves wit onic motionh
d
t
d a t d a t
a
.
The amplitude is |a|. 2The period is
The frequency is the number of oscillations per unit time. It is the reciprocal of the period.
2
2f
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cosd a tSimple harmonic motion can be expressed with either sine or cosine but since this object starts at 4 when t = 0, cosine makes sense. If you used sine, you'd have to use a phase shift to have a different value than 0 at t = 0.
4cosd t2
2T
2
2
4cosd t
x
y
x
An object attached to a coiled spring is pushed up a distance 4 units from its rest position and then released. Assuming that the motion is simple harmonic with period 2 seconds, write an equation that relates the displacement d of the object from its rest potion after t seconds. Assume that the positive direction of the motion is up.
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If we knew the equation of motion for an object, we could determine some things about it.
The equation modeling the motion of an object is:
This negative tells us that after t = 0, it will be stretched down first
x
Since we know , we can find the period
2 2
4 2T
3sin 4d t
This tells us that the motion will repeat
every seconds. 1.62
x
1.6
What is the frequency?
It is the reciprocal of the period so 2
.64
This means in one second, it has completed .64 oscillations.
x
.64