Trigonometric Ratios - Murphymath Page 2
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3B. The Three Basic Trigonometric Ratios
θ , pronounced “theta”, is a Greek letter which is commonly used in
The symbol
Trigonometry to represent an angle, and is used in the definitions below. Treat it as you
would any other variable.
θ
If
is an acute angle of a right triangle, then:
Trigonometric
Abbreviation
Ratio of the
Function
Following Lengths
θ
The
leg
opposite
angle
θ
θ
The sine of
=
sin(
)
=
The
hypotenuse
θ
The
leg
adjacent t
o
angle
θ
The cosine of θ
=
cos(
)
=
The
hypotenuse
θ
The
leg
opposite
angle
θ
θ
=
tan(
)
=
The tangent of
θ
The
leg
adjacent t
o
angle
*Note: A useful mnemonic (in abbreviated form) for remembering the above chart is:
SOH-CAH-TOA
SOH stands for s in( θ ), O pposite, H ypotenuse:
θ
=
Opposite
sin(
)
Hypotenuse
CAH stands for c os( θ ), A djacent, H ypotenuse:
θ
=
Adjacent
cos(
)
Hypotenuse
θ
θ
=
Opposite
TOA stands for t an(
), O pposite, A djacent:
tan(
)
Adjacent
C. Examples
First find the missing side length of each triangle (by using the Pythagorean Theorem, or one
of our theorems about Special Right Triangles, if applicable). Then find the indicated
trigonometric ratios. Pay close attention to which angle is being referenced!
B
=
=
1.
a)
sin( A
)
______
d)
sin(B
)
______
3
=
=
b)
cos(A
)
______
e)
cos(B
)
______
A
C
=
=
c)
tan( A
)
______
f)
tan(B
)
______
4
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