How to Teach Trig Functions

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How to Teach Trig Functions

• Sarah Benoit

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Planning this Lesson

• Inspiration
• Help organize my thoughts
• Think about what I am wanting to teach
• What is this for
• Unit/Chapter?
• Section?

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(No Transcript)
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The Key to Trigonometry

• Trigonometric Functions

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Things to Know

• Definition
• Relationship between angles of a triangle
• Ratios of the sides of the triangle
• How is the angle represented?
• Theta ? ?

• Trig Names
• Sine ? Sin ?
• Cosine ? Cos ?
• Tangent ? Tan ?
• Reciprocal Names
• Cosecant ? Csc ?
• Secant ? Sec ?
• Cotangent ? Cot ?

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Trig Functions

• Sin ?
• Opposite/Hypotenuse
• Cos ?
• Adjacent/Hypotenuse
• Tan ?
• Opposite/Adjacent
• Sin ?/Cos ?
• Helpful Hint
• SOHCAHTOA

Opposite
Hypotenuse
?
Adjacent
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Reciprocals of Trig Functions

• Csc ?
• 1/Sin ?
• Hypotenuse/Opposite
• Sec ?
• 1/Cos ?
• Hypotenuse/Adjacent
• Cot ?
• 1/Tan ?
• Adjacent/Opposite
• Cos ?/Sin ?

Opposite
Hypotenuse
?
Adjacent
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On Your Own
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• Hypotenuse

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• Adjacent

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• Opposite

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• Sin ? ?

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• Cos ? ?

• Tan ? ?

?

• Csc ? ?

• Sec ? ?

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• Cot ? ?

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Unit Circle
Y
(Cos ?,Sin ?)
(x,y)
(Cos ?/4,Sin ?/4)
?
?/4
X
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Unit Circle
(0,1)
(1/2, v3/2)
(-1/2, v3/2)
?/2
?/3
2?/3
(v2/2, v2/2)
(-v2/2,v2/2)
?/4
3?/4
(-v3/2, 1/2)
(v3/2, 1/2)
?/6
5?/6
0
?
(1,0)
(-1,0)
2?
7?/6
11?/6
(-v3/2,-1/2)
(v3/2,-1/2)
5?/4
7?/4
4?/3
(-v2/2, -v2/2)
(v2/2,- v2/2)
5?/3
3?/2
(-1/2, -v3/2)
(1/2, - v3/2)
(0, -1)
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Graph of Cos ? and Sec ?

• Things to Consider
• Amplitude?
• Period?
• Y-intercept?
• Asymptotes?
• Differences?
• Between function and its inverse
• Green Globs

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Graph of Sin ? and Csc ?

• Things to Consider
• Period?
• Amplitude?
• Asymptotes?
• Differences?
• Between function and its inverse
• Green Globs

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(No Transcript)
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Cos and Sin Wave
Geometer Sketchpad
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Graph of Tan ? and Cot ?

• Things to Consider
• Asymptotes?

• Differences?
• Between function and
• its inverse

• Green Globs

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(No Transcript)
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Tangent on a Circle
Geometer Sketchpad
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Now What?

• Play Green Globs
• Expert Mode
• What type of equations should I use?
• Trig Functions
• Previous forms of equations you know

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What if I still need help?

• Ask for help
• Websites
• http//www.drmath.com/
• http//www.gomath.com/
• Play Green Globs
• AND..

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Practice
Practice
PRACTICE PRACTICE PRACTICE
Practice
Practice
TO BECOME AN EXPERT OF TRIG FUNCTIONS
PRACTICE
Practice
Practice
Practice