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
Trigonometrythe 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.
leg
hypotenuse
leg
Name the hypotenuse. Name the legs.
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Opposite or Adjacent?
west

• 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.

orange
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Triangle Parts
Opposite side
hypotenuse
Adjacent side
c
Looking from angle B Which side is the
opposite? Which side is the adjacent?
a
b a
b
Opposite 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
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Trigonometric ratios
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Trigonometric ratios and definition abbreviations
SOHCAHTOA
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Express each trig ratio as a fraction
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5
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sin L sin J cos L tan J
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
What are the sides from angle Y?
opp
adj
hyp
15 sin 42 y y 10.04
15 cos 42 x x 11.1471723811.15
SOHCAHTOA
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Find x and y
hyp
adj
opp
SOHCAHTOA
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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