11.6: Sine, Cosine, Tangent

Review/PracticeTrig Ratios

Chapter 11Section 6

What is the mnemonic devise

that helps us remember the three

basic trig ratios?SOH CAH TOA

What is the definition of the sine

ratio?

sinopposite leg

Ahypotenuse

What is the definition of the

cosine ratio?

cosadjacent leg

Ahypotenuse

What is the definition of the tangent ratio?

tanopposite leg

Aadjacent leg

What trigonometric ratio is needed to

solve for x?

tanopposite leg

Aadjacent leg

x

19

15

What trigonometric ratio is needed to

solve for x?

sinopposite leg

Ahypotenuse

x

4.6

38

What trigonometric ratio is needed to

solve for x?

cosadjacent leg

Ahypotenuse

x4.652

Finding the Decimal or the Degree

If you have a decimal and need the degree use INVERSE.

Sin(-1), Cos(-1), Tan(-1)

If you have a degree and need the decimal use the STANDARD.

Sin, Cos, Tan

Find the angle whose tangent is

approximately .3057 and round to the nearest degree.

17

Find the angle whose sine is

approximately .7986 and round to the nearest degree.

53

Find the angle whose cosine is approximately .1564 and round to the

nearest degree.

81

Find the sine of 38o round to four decimal

places.

.6157

Find the tangent of 80o round to four decimal

places.

5.6713

Find the cosine of 10o round to four decimal

places.

.9848

Identify the trig function needed to solve:

41

x

18

cosine

41

x

18

Show the evaluation needed to solve:

cos 41 18

1 x

41

x

18

Solve for x:

cos 41 18

1cos 41( ) 18

18

cos 4123.85

xx

x

x

Identify the trig function needed to solve:

68x

24

tangent

68x

24

Show the evaluation needed to solve:

tan 68 24

1 x

Solve for x:

tan 68 24

1tan 68( ) 24

24

tan 689.7

xx

x

x

68x

24

Identify the trig function needed to solve:

80

x18.7

sine

Show the evaluation needed to solve:

sin80

1 18.7

x

80

x18.7

Solve for x:

sin80

1 18.7sin80(18.7)

18.42

x

x

x

80

x18.7

Identify the trig function needed to solve:

x

3.5

8.1 cosine

Show the evaluation needed to solve:

3.5cos

8.1x

x

3.5

8.1

Solve for x:

1

3.5cos

8.1

cos (3.5 / 8.1)

64.4

x

x

x

x

8.1

3.5

Identify the trig function needed to solve:

x

5.9

5.3 tangent

Show the evaluation needed to solve:

5.9tan

5.3x

x

5.9

5.3

Solve for x:

1

5.9tan

5.3

tan (5.9 / 5.3)

48

x

x

x

x

5.9

5.3

Finished! Finished

! Finished!Be sure to know all of

this for your test!