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5.3. Solving Trig Equations.notebook
February 17, 2012
The Ferris Wheel Story
LESSON 5.3. SOLVING TRIGONOMETRIC EQUATIONS
True or false:
False
False
1.] 2sin(y) = sin(2y) 2.] cos2(y) = cos(y2)
3.] 3tan(x2) ­ 5tan(x2) = ­ 2 tan (x2) True
4.] cos(3y) + cos(y) = cos (4y) False
5.] cos(y) + cos(x) = cos (x+y) False
6.] sin2(3x) = (sin (3x))2 True
The 1893 Chicago World’s Fair is considered the birthplace of the classic amusement park ride, the
Ferris wheel. The architectural wonder was created by an American engineer named George Ferris. The
original Ferris wheel no longer exists. But, in 1990, a new Ferris wheel was built at Navy Pier in Chicago
to resemble the original. While the Navy Pier Ferris Wheel is a beautiful Chicago landmark, its grandeur
actually pales in comparison to Mr. Ferris’ creation.
The Ferris wheel built for the World’s Fair had a diameter of 250 feet. It stood 14 feet off the ground.
It had 36 wooden boxcars that were the size of train cars. Each car could hold 60 people! The wheel
would load cars in such a way that each rider could enjoy a full rotation that lasted about 6 minutes.
The Ferris wheel at Navy Pier has a diameter of 140 feet. It stands 30 feet off the ground. The wheel
has 40 gondolas that seat six passengers each. It takes about 6 minutes for the Navy Pier Ferris Wheel
to complete one rotation.
Above is a picture of the first Ferris wheel next to the Ferris wheel at Navy Pier.
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Using the given information, the equations representing the two Ferris Wheels are as follows
World's Fair Ferris Wheel Navy Pier Ferris Wheel
Imagine the Navy Pier and the World’s Fair Ferris Wheel being
built beside each other. If you got on the Navy Pier Ferris Wheel
at the same time that your best friend got on the World's Fair
Ferris Wheel, when would you be at the same height?
If the wheels are turning at the same speeds, at what times over
a 15 minute time period would you be at the same height?
However, due to a cyclical pattern of trigonometric functions there will be infinitely many solutions. Feb 14­2:58 PM
Feb 14­8:14 PM
Lesson 5.3. Solving Trigonometric Equations (Easy cases)
When solving a trigonometric equation, your goal is to isolate the trigonometric function involved in the equation using standard algebraic operations and trigonometric identities. So, how many times will the two Ferris Wheels be at the same height over the course of 15 minutes?
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When solving algebraic equations, we can always CHECK (code word for verify) solutions.
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5.3. Solving Trig Equations.notebook
Verifying solutions for Trig Equation:
Example: Verify that each x value is a solution of the equation given:
February 17, 2012
SOLVING EQUATIONS.
Find solutions for the following trigonometric equations on interval and ALL general solutions. 1.] 2 cos(x) – 1 = 0 (a) x = π/3 (b) x = 5π/3
2.] sec x – 2 = 0 (a) x = π/3 (b) x = 5π/3
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Equations of Quadratic type:
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5.3. Solving Trig Equations.notebook
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February 17, 2012
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Extracting Square Roots:
Remember to use ± when taking the square root!!!
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Rewriting as a Single Trigonometric Function:
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5.3. Solving Trig Equations.notebook
February 17, 2012
Functions of Multiple Angles:
Remember to use ± when taking the square root!!!
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Feb 16­8:42 AM
Try these in your groups: Page 364/ 1, 3, 5
Page 364/ 7, 13, 17, 23, 29
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OTL Page 364/22­30 EVEN
Page 366/ 68, 72
TAKE HOME TEST
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