Download Lesson 118: Sine, Cosine, Tangent

Bell Work:
Perform the calculation and
express the answer with the
correct number of significant digits.
1.24g + 6.4g + 5.1g
Answer:
12.7g
Lesson 118:
Sine, Cosine, Tangent
In lesson 112, we practiced finding
the ratios of lengths of sides of
right triangles. These ratios have
special names.
Trigonometry Ratios:
Name
Ratio
Sine
Opposite/Hypotenuse
Cosine
Adjacent/Hypotenuse
Tangent
Opposite/Adjacent
SOH
CAH
TOA
Example:
Find the sine, cosine and tangent
B
of <A.
10
A
6
C
8
Answer:
Sine <A = 6/10 = 0.6
Cosine <A = 8/10 = 0.8
Tangent <A = 6/8 = 0.75
Notice that we express each ratio as
a decimal. The “trig” ratios for this
angle happen to be rational numbers.
Since many right triangles involve
irrational numbers, the trig ratios for
many angles are irrational. We
express the irrational ratios rounded
to a selected number of decimal
places.
Example:
Find the sine, cosine and tangent
S
of <R.
R
30°
T
Answer:
Sine 30° = ½ = 0.5
Cosine 30° = √3/2 ≈0.866
Tangent 30° = 1/√3 ≈ 0.577
We can find the decimal values of trig
ratios on a calculator. For the ratios in
the last example, a calculator with a
square root key is sufficient. For
other angles we can use the trig
functions on a scientific or graphing
calculator, which are often
abbreviated with three letters.
Name
Abbreviation
Sine
sin
Cosine
cos
Tangent
tan
If you have a calculator with these
three keys, practice using them for
the triangle in the last example. To
find the sine of a 30° angle type in
sin(30). The display should read 0.5.
try again with that cosine and tangent
of 30°. Compare the results to the
last answer.
Example:
Use a calculator to find the since
and cosine of <A.
1
A
35°
Answer:
Sine 35° = opp/hyp = 0.574/1
Cosine 35° = adj/hyp = 0.819/1
Trig ratios can help us calculate
measures we cannot perform directly.
Suppose we want to find the height of
a tree. If the angle of elevation from
100 feet away is 22°, we can find the
height of the tree using the tangent
function.
Example:
Find the height of the tree.
Answer:
Tangent 22° = opp/adj
= Tree height/100 feet
= 0.404/1
t
100
= 0.404
1
The height of the tree is about 40.4 feet
HW: Lesson 118 #1-25