7-3A Trigonometric Ratios
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7-3A Trigonometric Ratios
What is trigonometry?
What is sine?
What is cosine?
What is tangent?
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Definition
Trigonometry—the study of the special relationships between the angle measures and the side lengths of right triangles.
Trigonometric ratios are ratios of side lengths in right triangles.
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Right triangle parts.
AB
leg
leghypotenuse
A
B
C
Name the hypotenuse.
Name the legs. ACBC,
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Opposite or Adjacent?
• The opposite of east is ______
• The door is opposite the windows.
• In a ROY G BIV, red is adjacent to _____
• The door is adjacent to the cabinet.
west
orange
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Triangle Parts
A
B
C
a
b
c
Opposite sideAdjacent side
hypotenuseOpposite side
Adjacent side
Looking from angle A:
Which side is the hypotenuse?
Which side is the opposite?
Which side is the adjacent?
c
a
b
Looking from angle B:
Which side is the opposite?
Which side is the adjacent?
b
a
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Trigonometric ratios
hypotenuseoflength
Aoppositelegoflengthsine Aof
c
a
AB
BC
A
B
C
a
b
c
hypotenuseoflength
Aoppositelegoflengthcosine Aof
c
b
AB
AC
Atoadjacentlegoflength
Aoppositelegoflengthtangent Aof
b
a
AC
BC
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Trigonometric ratios and definition abbreviations
c
aA
hypotenuse
oppositesin
c
bA
hypotenuse
adjacentcos
A
B
C
a
b
c
b
aA
adjacent
oppositetan
SOHCAHTOA
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Express each trig ratio as a fraction
13
5
13
12
J
K
L
5
12
13
sin L
sin J
cos L
tan J
13
12
5
12
SOHCAHTOA
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Using a scientific calculator to find the value of a trig ratio for an angle
Calculators must first be in degree mode for trig values.
If your calculator is not in degree mode, raise your hand.
Graphing calculators need to be changed to degrees.
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Find the cos of 58°
Enter: 58 cos = Enter: cos 58 =
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Find the values of x and y
1542cos
x
1542sin
yxy
Z
X Y15
42°
15 cos 42° = x
x ≈ 11.14717238≈11.15
15 sin 42° = y
y ≈ 10.04
oppadj
hyp
What are the sides from angle Y?
SOHCAHTOA
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Find x and y
y
2670sin
x
2670tan
70°xy
26
SOHCAHTOA
opp
adj
hyp
67.2770sin
26
2670sin
y
y
y
46.970tan
26
2670tan
x
x
x
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What is trigonometry?The study of the special relationships between the angle measures and the side lengths of right triangles.What is sine?Side opposite over hypotenuse.What is cosine?Side adjacent over hypotenuse.What is tangent?Side opposite over side adjacent.
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Assignment 7-3A
Page 514, 1-15