Trigonometry Basics

By Ross MacBethEd. 205 Section 06

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Main• Introduction• What is Trigonometry?• Sine Function• Cosine Function• Tangent Function• Pythagorean Theorem• Review

– Sine Function Problem• Solution

– Cosine Function Problem• Solution

– Tangent Function Problem• Solution

– Pythagorean Theorem Problem• Solution

– Harder Problem• Solution

• Resources• Concept Map

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Ross MacBeth• I am a senior at Grand Valley and am

the president of Vertical Earth, Grand Valleys rock climbing club. I have been climbing for about 5 years now and have a deep passion for the sport. Through climbing I have gotten the opportunity to travel all over the country and have seen some amazing things. This has led to a love of travel that I hope will last my entire life. I grew up on the east side of Michigan and while family is very important to me I hope to move outside of Michigan someday.

For any questions please email me at macbethr@student.gvsu.edu

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What is Trigonometry?

• Trigonometry is the study of triangles. Using trig you can solve many problems percisely where you may have only been able to aproximate before. Trig is used in everything from engineering and archetecture to G.P.S.

• In this lesson we will only be studying right triangles, meaning only triangles with a right angle as one of their 3 angles.

• The longest side is known as the hypoteneuse and the other two sides are refered to as “legs.”

• Watch a video of solving trignometric functions here.

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The Sine Function

• The Sine function is often denoted “sin”

• It can help find the length of an opposite side or hypoteneuse when the other is known.

• sin(Θ) = Opposite/hypoteneuse.

θ

opposite

hypoteneuse

adjacent

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The Cosine Function

• The cosine function is often denoted “cos”

• It can help find the length of an adjacent side or hypoteneuse when the other is known.

• cos(Θ) = adjacent/hypoteneuse.

θ

opposite

adjacent

hypoteneuse

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The Tangent Function

• The tangent function is often denoted “tan.”

• It can help find the length of an adjacent side or opposite side when the other is known.

• tan(Θ) = opposite/adjacent

θ

opposite

adjacent

hypoteneuse

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The Pythagorean Theorem

• It can help find the length of any side when the other two lengths are known

θ

b

a

c

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Review

Sine problem

Cosine problem

Tangent problem

Pythagorean Theorem problem

Extra hard problem

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Solution

30

6X

What is the length of side X?

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Solution

45

What is the length of the side X?

X

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17

17

What is the angle of θ

θ

Solution

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Solution

3

4

What is the length of the hypoteneuse?

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θ

1

2

What is θ?

Solution

Hard ProblemQuit

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Resources

http://www.cs.utah.edu/~draperg/cartoons/jb/watson.html

http://outkasty.files.wordpress.com/2007/10/trigonometry.jpghttp://www.sandomenico.org/uploaded/photos/Library/blackboard_math.gif

http://www.youtube.com/watch?v=lvP96cTBiBY

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Concept Map Quit