Trigonometry
The branch of mathematics that deals with the relations
between the sides and angles of plane or spherical
triangles, and the calculations based on them
The Six Trig Functions
Hipparchus of Nicaea
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He made an early formulation of
trigonometry
Introduced an important idea into
trigonometry-the model of a circle
containing 360 degrees
Hipparchus is considered the greatest
ancient astronomical observer
Has solved several problems of spherical
trigonometry
His achievements:
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first to develop a reliable method to predict solar
eclipses
discovered precession
compiled first comprehensive star catalog of the
western world
possibly invented the astrolabe
Ferris Wheel
• Suppose Sarah wants to take a Ferris
wheel ride at a local carnival. The
Ferris wheel has a height of 65.5
meters and a diameter of 61.5
meters. It takes the Ferris wheel 4.5
minutes to make one revolution.
Sarah starts her ride at the midline
at exactly 12:30 pm, once all of the
other passengers are loaded. Write
the sinusoidal equation that models
the height of Sarah’s chair at any
time, t. When does she reach a
height of 55 meters?
Ferris Wheel
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You can use the general equation y = Asin(kt - c) + h to find
the sinusoidal function of this Ferris wheel.
Amplitude, or A, is the radius of the Ferris wheel.
To find k, you can use the fact that the period is equal to 4.5
minutes.
There is no phase shift because at t = 0 the seat is at the
midline.
To find h, you need to find the bottom of the Ferris wheel.
You know that the total height is 65.5 meters and the
diameter is 61.5 meters. To find the bottom portion of the
Ferris wheel, you can subtract the diameter of the Ferris
wheel from the total height.
65.5 – 61.5 = 4 meters
The value of h at the midline is the amplitude plus the bottom
of the Ferris wheel.
30.75 + 4 = 34.75 meters
The final equation is:
Ferris Wheel Example
• To find out when the Ferris wheel reaches a height of 55 meters, solve the
equation for t when y = 55.
Remember to make sure your calculator is set on radian mode.
Sarah will reach a height of 55 meters 0.515 minutes after she starts her
ride.
Convert the minutes into seconds:
.515 mintues x seconds
If Sarah starts her ride at 12:30 pm, then she will reach a height of 55
meters at approximately 12:30.31 pm.
Sinusoidal Function
-The height of a full rotation is
going to be between -1 and +1
-The circumference of the bicycle
wheel is 2∏
-If time=1, then it would take 2∏
seconds to complete a full
rotation, h(1)=2∏
• http://people.hofstra.edu/stef
an_waner/trig/wheel.html
Polar Coordinates in Real World
Setting
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Polar coordinates are often used in aviation
Expresses a position on a two dimensional
plane from an angle from a fixed direction
and distance from a fixed point
Can be converted by using Sine and Cosine
functions
By multiplying the coordinates by cosine, you
obtain x, if you multiply by sine, you can
obtain y
Works Cited
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http://aventalearning.com/content168staging/2008Trigonometry/unit4/html/secti
on_4_page_8.html
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http://www.regentsprep.org/Regents/math/algtrig/ATT1/trigsix.htm
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http://abyss.uoregon.edu/~js/glossary/hipparchus.html
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http://people.hofstra.edu/stefan_waner/trig/trig1.html
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http://justbasic.wikispaces.com/PolarCoords
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http://prezi.com/gj0mgvu_s2ec/real-life-applications-for-sine-and-cosinetrigonometric-fun/