Angles and their measure, Solving Right Triangle and Trigonometric Ratios
Lesson 5.3. Solving Trigonometric Equations (Easy cases) · 8/9/2012 · Lesson 5.3. Solving...
Transcript of Lesson 5.3. Solving Trigonometric Equations (Easy cases) · 8/9/2012 · Lesson 5.3. Solving...
5.3. Solving Trig Equations.notebook
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1.] 2sin(y) = sin(2y) 2.] cos2(y) = cos(y2)
3.] 3tan(x2) 5tan(x2) = 2 tan (x2)
4.] cos(3y) + cos(y) = cos (4y)
5.] cos(y) + cos(x) = cos (x+y)
6.] sin2(3x) = (sin (3x))2
LESSON 5.3. SOLVING TRIGONOMETRIC EQUATIONS
True or false:
FalseTrue
False
False False
True
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The 1893 Chicago World’s Fair is considered the birthplace of the classic amusement park ride, theFerris wheel. The architectural wonder was created by an American engineer named George Ferris. Theoriginal Ferris wheel no longer exists. But, in 1990, a new Ferris wheel was built at Navy Pier in Chicagoto resemble the original. While the Navy Pier Ferris Wheel is a beautiful Chicago landmark, its grandeuractually 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 wheelwould 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 wheelhas 40 gondolas that seat six passengers each. It takes about 6 minutes for the Navy Pier Ferris Wheelto complete one rotation.
Above is a picture of the first Ferris wheel next to the Ferris wheel at Navy Pier.
The Ferris Wheel Story
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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?
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However, due to a cyclical pattern of trigonometric functions there will be infinitely many solutions.
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So, how many times will the two Ferris Wheels be at the same height over the course of 15 minutes?
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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.
When solving algebraic equations, we can always CHECK (code word for verify) solutions.
5.3. Solving Trig Equations.notebook
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Verifying solutions for Trig Equation:
Example: Verify that each x value is a solution of the equation given:
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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SOLVING EQUATIONS.
Find solutions for the following trigonometric equations on interval and ALL general solutions.
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Equations of Quadratic type:
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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
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Remember to use ± when taking the square root!!!
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Functions of Multiple Angles:
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Try these in your groups:
Page 364/ 1, 3, 5
Page 364/ 7, 13, 17, 23, 29
OTL Page 364/2230 EVEN Page 366/ 68, 72
TAKE HOME TEST
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