Trigonometric Ratios Worksheet Page 4
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221.2 Sine, Cosine, and Tangent of Angles from 0
to 360
°
°
KEY CONCEPTS
• For any rotation angle in standard position that has
y
a point P(x, y) on its terminal arm, the primary
P(x, y)
y
__
r ,
trigonometric ratios for the angle are sin =
_______
y
x
__
__
r , and tan =
x , where r =
√
.
2
+ y
2
r
cos =
x
• Pairs of related angles can be found using the
x
0
coordinates of the endpoints of their terminal arms
and a reference angle in quadrant I.
Example
The coordinates of a point on the terminal arm of an angle in standard position are
G(−3, −5). Determine the exact primary trigonometric ratios for .
Solution
Plot G(−3, −5) on a coordinate grid.
y
6
4
2
�3
x
0
2
4
6
�6
�4
�2
�2
�5
r
�4
Determine r.
G(�3, �5)
�6
_______
√
x
2
+ y
2
r =
_____________
√
( −3)
2
+ ( −5)
2
r =
___
r =
√
3
y
y
x
__
__
__
sin =
r
cos =
r
tan =
x
−5
−3
−5
____
____
___
___
=
___
=
=
−3
√
3
√
3
5
3
5
____
____
__
= −
___
= −
___
=
3
√
3
√
3
MHR • Chapter 1 978-0-07-090893-2
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