7-3A Trigonometric Ratios What is trigonometry? What is sine? What is cosine? What is tangent?

7-3A Trigonometric Ratios

What is trigonometry?

What is sine?

What is cosine?

What is tangent?

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.

Right triangle parts.

AB

leg

leghypotenuse

A

B

C

Name the hypotenuse.

Name the legs. ACBC,

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

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

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

Trigonometric ratios and definition abbreviations

c

aA

hypotenuse

oppositesin

c

bA

hypotenuse

adjacentcos

A

B

C

a

b

c

b

aA

adjacent

oppositetan

SOHCAHTOA

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

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.

Find the cos of 58°

Enter: 58 cos = Enter: cos 58 =

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

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

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.

Assignment 7-3A

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