2. Important Idea
Trigonometry, which means
triangle measurement was
developed by the Greeks in
the 2nd
century BC. It was
originally used only in
astronomy, navigation and
surveying. It is now used to
model periodic behavior such
as sound waves and
planetary orbits.
6. Important Idea
Angles may be measured in
degrees where 1 degree (°)
is 1/360 of a circle, 90° is ¼
of a circle, 180° is ½ of a
circle, 270° is ¾ of a circle
and 360° is a full circle. A 90°
angle is also called a right
angle.
12. Try This What is the
measure of this
angle?
a. 0°
b. 45°
c. 90°
d. 120°
e. 180°
13. Try This What is the
measure of this
angle?
a. 0°
b. 45°
c. 90°
d. 120°
e. 180°
14. Try This What is the
measure of this
angle?
a. 0°
b. 45°
c. 90°
d. 120°
e. 180°
15. Try This What is the
measure of this
angle?
a. 0°
b. 45°
c. 90°
d. 120°
e. 180°
16. Try This What is the
measure of this
angle?
a. 0°
b. 45°
c. 90°
d. 120°
e. 180°
17. Definition
Fractional parts of a degree
can be written in decimal
form or Degree-Minute –
Second (DMS) form. A
minute is 1/60 of a degree. A
second is 1/60 of a minute.
How many seconds are in
each degree?
18. Example
Write 29°40’20” in decimal
degrees accurate to 3
decimal places.
Symbol for
minute
Symbol
for second
19. Important Idea
To convert from DMS to
decimal, write the decimal
expression 29°40’20” as:
40 20
29
60 3600
+ +
in your calculator.
27. Important Idea
If 2 right triangles have
equal angles, the
corresponding ratios of
their sides must be the
same no matter the size of
the triangles. This fact is
the basis for trigonometry.
34. Definition
For a given acute angle in
a right triangle:
θ
The sine of written as
is the ratio
θ sinθ
sinθ =
opposite
hypotenuse
(see p.416 of your text):
M
em
orize
35. Definition
For a given acute angle in
a right triangle:
θ
The cosine of written asθ
cosθ
cosθ =
adjacent
hypotenuse
is the ratio:
(see p.416 of your text):
M
em
orize
36. Definition
For a given acute angle in
a right triangle:
θ
The tangent of written asθ
tanθ
tanθ =
opposite
adjacent
is the ratio:
(see p.416 of your text):
M
em
orize
37. opposite
Definition
For a given acute angle in
a right triangle:
θ
The cosecant of written asθ
cscθ
1
csc
sin
θ
θ
= = hypotenuse
is the ratio:
(see p.416 of your text):
M
em
orize
38. adjacent
Definition
For a given acute angle in
a right triangle:
θ
The secant of written asθ
secθ
1
sec
cos
θ
θ
= = hypotenuse
is the ratio:
(see p.416 of your text):
M
em
orize
39. opposit
e
Definition
For a given acute angle in
a right triangle:
θ
The cotangent of written
as
θ
cotθ
1
cot
tan
θ
θ
= = adjacent
is the ratio:
(see p.416 of your text):
M
em
orize
49. Consider the first two
special angles in degrees...
30°
60°
Long Side ShortSide
Hypotenuse
Analysis
50. Important Idea
In a 30°-60°-90° right
triangle, the short side is
opposite the 30° angle, the
long side is opposite the 60°
angle, and the hypotenuse
is opposite the 90° angle.
72. Lesson Close
We will use the information in
this lesson to solve right
triangle problems in the next
lesson. Right triangle
problems are used in real-
world applications such as
indirect measurement,
surveying and navigation.
Editor's Notes
.576 x 60=34.56’; .56 x 60=33.6’’ round to 34 ‘’: 37deg34min34sec