Practical Trig
Preliminary Definitions
•
A
Right Triangle:
Any triangle that possesses two sides separated by a
90
◦
angle.
•
The
reference angle (
θ
):
One of the two remaining angles of a right
triangle (
θ
= 90
◦
).
•
The
hypotenuse (hyp):
The side of a right triangle opposite the 90
◦
angle.
•
The
opposite side (opp):
The side of a right triangle opposite the
reference angle (
θ
).
•
The
adjacent side (adj):
The side of a right triangle adjacent the refer
ence angle (
θ
)
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Primary Trig Functions
Each trig function is defined (
≡
) as a ratio of the lengths of two sides of a right
triangle.
Generalize “hyp”, “opp” and “adj” to mean the lengths of the hy
potenuse, opposite and adjacent sides of a right triangle, respectively. Then. . .
sin
θ
≡
opp
hyp
cos
θ
≡
adj
hyp
tan
θ
≡
opp
adj
Less Important Trig Functions
While these functions are also ratios of the lengths of the sides of a right triangle,
you’ll usually see them defined in terms of the primary trig functions. Because
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 Spring '10
 Buchanan
 Trigonometry, Right triangle, Inverse function, Inverse trigonometric functions, tan θ

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