Download 7.4 The Sine and Cosine Ratios

MPM2D1
7.4 Sine and Cosine Ratios (Continued from 7.3 activity)
a) How are the Type 2 Ratios related?
b) This ratio is called the sine ratio for angle E. How would you clearly and accurately
explain to someone which sides of the triangles you used to form the sine ratio?
Use a sketch if necessary.
c) How are the Type 3 Ratios related?
d) This ratio is called the cosine ratio for angle E. How would you clearly and
accurately explain to someone which sides of the triangles you used to form the
cosine ratio? Use a sketch as well if necessary.
Rule: For an acute angle A in a right triangle, the primary trigonometric ratios are defined
as follows: Sine, Cosine and Tan.
B
A
C
Example 1:
Evaluate each ratio to the nearest thousandth (3 decimal place).
a)
tan 48
=
b)
c)
e)
sin 89
sin 17
=
=
d)
f)
cos 65
cos 11
tan 73
=
=
=
1
Example 2: We can also use the primary trigonometric ratios to find angle measurements.
D
19m
13 m
E
F
If we want to determine the measure of
F, we would use the sine ratio because we
are given the measures of the sides ______
and _________ to the angle.
 sin F =
Example 3:
Find each angle measure to the nearest degree. (Use sin-1, cos-1 or tan-1)
a)
tan A  2.547
A=
b)
cos B  0.655
B=
c)
sin C  0.489
C=
d)
tan D  0.498
D=
e)
sin E  0.123
E=
f)
cos F  0.328
F=
Example 4:
Z
Y
5
X
4
Example 5:
M
In XYZ find the measures of X and Z .
In MNO , find the length of MN , to the nearest tenth.
9cm
O
38˚
N
Example 6: Solve a Right Triangle (Note: Solving a triangle means finding all the missing
sides and angles)
Solve ΔABC, Round side lengths to the nearest unit and angles to the nearest degree.
p. 372-375 -work through
examples
CYU #1
Practice #1-4ac, 6-7ac, 8-9,
11ac, 15,16, 20,21,24, 32
2