Trigonometric Functions - Unit Circle Approach Worksheet

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Section 6.2 – Trigonometric Functions: Unit Circle Approach
The unit circle is a circle of radius 1 centered at the origin. If we have an
angle in standard position superimposed on the unit circle, the terminal side
will intersect the unit circle at a particular point. The point of intersection will
depend on the value of the angle. This implies that the x-coordinate and the
y-coordinate of the point will depend on the value of the angle.
(
)
0, 1
3
1
(
)
3
1
(
)
,
,
2
2
2
2
π
π
2
2
(
)
2
2
(
)
2
,
,
3
3
2
2
2
2
π
90˚
120˚
60˚
4
3
1
4
(
)
3
1
(
)
,
,
135˚
45˚
2
2
2
2
π
6
6
150˚
30˚
(
)
(
)
0
π
180˚
1, 0
– 1, 0
330˚
210˚
11π
3
1
(
)
, –
225˚
3
1
(
)
315˚
6
6
, –
2
2
2
2
240˚
270˚ 300˚
4
2
2
(
)
4
2
2
(
)
, –
, –
2
2
3
2
2
3
2
1
3
(
)
3
1
(
)
, –
, –
2
2
2
2
(
)
0, – 1
Thus, for an angle that measures 30˚ in standard position, the terminal side
3
1
(
)
will pass through the point
,
on the unit circle. For an angle that
2
2
measures 270˚ in standard position, the terminal side will pass through the
point (0, – 1) on the unit circle. Since the x- and y-coordinates of the point
on the unit circle intersected by the terminal side depend on the measure of
the angle, we can define each coordinate as a function of the angle.

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