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Chapter 11, Section 6: Sine, Cosine, and Tangent. Basic Trig ratios.
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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!