Download Trigonometric Functions and Triangles

Next, we convert 22:80 into degrees using a similar technique.
1 = 600 () 10 =
1
60
So
22:8
60
= :38
22:80
=
Therefore, 30 220 4500 = 30 22:80 = 30:38
Remark 7 To convert DMS to decimal degrees, we divide the number of seconds by 60 and add the result to the number of minutes. This gives us the
decimal minutes. We then divide the decimal minutes by 60 and add the result
to the number of degrees. This gives us the angle measure using decimal degree
notation.
Example 8 Convert 30:38 to DMS notation.
We use the fact that 1 = 600 therefore, :38 = :38 600 = 22:80 (that is 220 and
:80 ). Now, we convert the decimal minutes to seconds using a similar technique.
10 = 6000 therefore :80 = :8 6000 = 4800 . It follows that 30:38 = 30 220 4800 .
Remark 9 Scienti…c calculators can also do this automatically. See the manual
for your calculator to learn how to do it.
1.2
Angles, Points and the Unit Circle
De…nition 10 (Unit Circle) The Unit Circle is the circle of radius 1, centered at the origin (the point with coordinates (0; 0)).
The equation of the unit circle is
x2 + y 2 = 1
This means that a point with coordinates (x; y) is on the unit circle if and only
if its coordinates satisfy x2 + y 2 = 1.
Example 11 Is the point with coordinates (1; 2) on the unit circle?
we see that 12 + 22 = 1 + 4 = 5 6= 1. Therefore, the point with coordinates (1; 2)
is not on the unit circle.
p p !
2
2
;
on the unit circle?
Example 12 Is the point with coordinates
2
2
We see that
p !2
p !2
2
2
2 2
+
=
+
2
2
4 4
=
=
4
4
4
1