Angle of Elevatio

n

The angle of elevation is measured from a horizontal line looking up at something.

The Angle of Depression is measured from a horizontal line looking down at something.

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

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

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

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.

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