Transcript Trig Functions

Introduction
to Trigonometry
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!
Right Triangle
Opposite
Hypotenuse
Adjacent
A
Same Right Triangle – Different Angle
B
Adjacent
Hypotenuse
Opposite
Trig Definitions:
•
•
•
•
•
•
Sine
=
Cosine
=
Tangent =
Cosecant =
Secant
=
Cotangent =
opposite/hypotenuse
adjacent/hypotenuse
opposite/adjacent
hypotenuse/opposite
hypotenuse/adjacent
adjacent/opposite
A Way To Remember
• Sin = Opposite/Hypotenuse
Oprah Had
• Cos = Adjacent/Hypotenuse
A Huge
• Tan = Opposite/Adjacent
Old Afro
y
x,y
r
y
O
x
x
2
r = x
2
+y
2
Definitions of Trig Functions
•
•
•
•
•
•
Sin
Cos
Tan
Csc
Sec
Cot
O
O
O
O
O
O
=
=
=
=
=
=
y/r
x/r
y/x
r/y
r/x
x/y
The Unit Circle
Radius = 1
y
x,y
1
1/2
30
x
√3/2
2
r = x
2
+y
2
y
x,y
1
√/2/2
45
x
√2/2
2
r = x
2
+y
2
y
x,y
1
1/2
60
x
√3/2
2
r = x
2
+y
2
The Unit Circle-Special Angles
and Their Exact Values