Download Introduction to Trigonometry

Introduction to
Trigonometry
Lesson 9.9
What is Trigonometry?
• The shape of a right
triangle is determined
by the value of either of
the other two angles.
• This means that once
one of the other angles is
known, the ratios of the
various sides are
ALWAYS the same
regardless of the size of
the triangle.
• These ratios are
described by following
“trigonometric
functions” of the known
angle.
• This means that if one
angle and one side
length is known, all
other angles and side
lengths can be
determined.
• OR… it means that if
two sides of the
triangle are known, the
third side and all other
angles can be
determined.
Three Trigonometric
Ratios
B
a
c
A
b
1. Sine of A = sin A = opposite leg = a
c
hypotenuse
b
2. Cosine of A = cos A = adjacent leg =
c
hypotenuse
3. Tangent of A = tan A = opposite leg = a
adjacent leg b
C
S
O
H
C
A
H
T
O
A
Sine
Opposite
Hypotenuse
Cosine
Adjacent
Hypotenuse
Tangent
Opposite
Adjacent
Memorize
this…
Memorize
this…
S O H
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C A H T O A
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D Y
J P
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C E
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Find cos A
1. By the Pythagorean Theorem find side c.
2. c = 13
3. cos A = adjacent leg to A = 12
13
hypotenuse
Find tan B
1. tan B =
leg opposite B = 12
5
leg adjacent to B
ΔABC is an isosceles triangle
as marked. Find sin C.
1. Draw in an altitude to make a
A
right triangle.
25
25
2. Use the Pythagorean
20
Theorem to find the length
of the altitude.
B
15 30 15
3. AD = 20
4. Sin C = opposite = 20 = 4
hypotenuse 25 5
C
Use the fact that tan 40º ≈ 0.8391
to find the height of the tree to
the nearest foot.
• Tan 40º = opposite = h
adjacent 50
• 0.8391 ≈ h
50
• 0.8391(50) ≈ h
• 41.955 ≈ h
• The tree is ≈ 42 feet tall.
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