7.5 trig equations. the story! in the arctic, zoey wants to know how to dress! she has to dress...
TRANSCRIPT
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7.5 Trig Equations
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The Story!
In the arctic, zoey wants to know how to dress! She has to dress differently depending on the
temperature of the snow (degrees).
Find the temperature (degrees) in each equation!
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The process: How to find the temperature (X)
• Find a way to get your equation to equal zero (some equations already will, others will require changing the terms of the equation so that all of the variables are on one side and a zero is on the other side of the = sign)
• After getting it to zero, see if anything can be factored, simplified, or replaced by an identity. This will help you get X all alone.
• Break the parts of the equation up into terms of X• Solve each part for X and test the solutions in the
original equation
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Process: Z(FSR)BS
• Zero, Factor, Simplify, Replace, Break up, Solve
• Zoey Finds Snow Really BotherSome
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Example
Sin(x)Cos(x) = ½cos(x)
Step 1: Zero
Set equation equal to zero
Sin(x)cos(x) = ½cos(x) - ½cos(x) - ½cos(x)
Sin(x)cos(x) - ½cos(x) = 0
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Step 2: Factor
Sin(x)cos(x) - ½cos(x) = 0
Factor out Cos(x)
Cos(x){sin(x)- ½} = 0
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Step 3: Simplify
Cos(x){sin(x)- ½} = 0
Can this be simplified?
No!
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Step 4: Replace
Cos(x){sin(x)- ½} = 0Can anything be replaced by another identity?
No!
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Step 5: Break Up
Cos(x){sin(x)- ½} = 0
Break up the cos and the sin parts of the equation
Cos(x) = 0 and Sin(X) - ½ = 0
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Step 6: Solve
Cos(x) = 0 and Sin(X) - ½ = 0
Cos(X) = 0 when X = 90°
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Step 6 continued
Sin(X) - ½ = 0 Sin(X) = ½Sin(X) = ½ when X = 30 °
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Bibliography
• http://www.freemathhelp.com/trig-double-angles.html
• Glencoe, Advanced Mathematical Concepts, textbook