Introduction to Trigonometry

1
Introduction to Trigonometry
2
What is Trigonometry?

• Trigonometry is the study of how the sides and
  angles of a triangle are related to each other.
• It's all about triangles!

3
Right Triangle
Hypotenuse
Opposite
Adjacent
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Same Right Triangle Different Angle
B
Hypotenuse
Adjacent
Opposite
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Trig Definitions

• Sine opposite/hypotenuse
• Cosine adjacent/hypotenuse
• Tangent opposite/adjacent
• Cosecant hypotenuse/opposite
• Secant hypotenuse/adjacent
• Cotangent adjacent/opposite

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A Way To Remember

• Sin Opposite/Hypotenuse Oprah Had
• Cos Adjacent/Hypotenuse A Huge
• Tan Opposite/Adjacent
• Old Afro

7
y
x,y
r
y
x
x
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Definitions of Trig Functions

• Sin y / r
• Cos x / r
• Tan y / x
• Csc r / y
• Sec r / x
• Cot x / y

9
The Unit Circle
Radius 1
10

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y
x,y
1
1/2
x
v3/2
12
y
x,y
1
v/2/2
x
v2/2
13
y
x,y
1
1/2
x
v3/2
14
The Unit Circle-Special Angles and Their Exact
Values