Trigonometry Worksheet Page 6
ADVERTISEMENT
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22%
Note the strict inequalities. Angles that are exactly 0°, 90°, 180°, 270° or 360° (in radians: 0,
, ,
or
$
$
2 ) are called cardinal angles. They are not part of any quadrant.
The Trigonometric Functions
Let us look again at a unit circle (radius = 1) placed on an xy-axis system with its center at the origin. A
ray is drawn, intersecting the circle at point P as shown in Fig. 7. Let
represent the angle from the
positive x-axis to the ray.
Three definitions can now be made, each corresponding to a physical characteristic of the ray and its
intersection of the unit circle at point P:
DEFINITION:
• The cosine of , written cos , is the x-coordinate of P.
• The sine of , written sin , is the y-coordinate of P.
• The tangent of , written tan , is the slope of the ray.
Fig. 7
With these definitions, some immediate results can be determined for the cardinal angles based on the
unit circle:
• For 0° (0 radians), this is the point (1,0). Therefore, cos{0{ = 1, sin{0{ = 0 and the slope of
the ray is tan{0{ = 0.
2 radians), this is the point (0,1). Therefore, cos { 90 { = 0, sin { 90 { = 0 and since
• For 90° (
the ray is vertical, the slope is not defined (that is, tan {90{ is not defined).
• For 180° ( radians), this is the point (-1,0). Therefore, cos { 180 { = −1, sin { 180 { = 0 and the
slope of the ray is tan { 180 { = 0.
2 radians), this is the point (0,-1). Therefore, cos { 270 { = 0 , sin { 270 { = −1
• For 270° (3
and the slope of the ray is undefined since it is vertical.
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education