Trigonometric Functions - Unit Circle Approach Worksheet Page 3
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1214
Definition
If θ is an angle in standard position and if the terminal side of θ intersects
the unit circle at (x
, y
), then
uc
uc
y
uc
sin( θ ) = y
cos( θ ) = x
tan( θ ) =
uc
uc
x
uc
1
1
x
uc
csc( θ ) =
sec( θ ) =
cot( θ ) =
y
x
y
uc
uc
uc
1
1
1
Note that csc( θ ) =
, sec( θ ) =
, and cot( θ ) =
.
sin(θ)
cos(θ)
tan(θ)
Objective 1:
Find the Exact Values of the Trigonometric Functions
Using a Point on the Unit Circle.
Let P = (x, y) be the point on the unit circle that corresponds to t. Find
the values of the six trigonometric functions of t:
2
5
(
)
Ex. 2a
, –
Ex. 2b
(0, 1)
3
3
Solution:
5
2
a)
sin(t) = y
= –
cos(t) = x
=
uc
uc
3
3
5
−
y
5
2
5
3
5
÷
uc
3
tan(t) =
=
= –
= –
= –
•
x
2
3
3
3
2
2
uc
3
1
1
3
3 5
csc(t) =
=
= –
= –
y
5
5
5
uc
−
3
1
1
3
sec(t) =
=
=
2
x
2
uc
3
2
2
3
2
2 5
x
(
)
uc
3
cot(t) =
=
=
–
= –
= –
•
y
3
5
5
5
5
uc
−
3
b)
sin(t) = y
= 1
cos(t) = x
= 0
uc
uc
y
1
uc
tan(t) =
=
which is undefined
x
0
uc
1
1
csc(t) =
=
= 1
y
1
uc
1
1
sec(t) =
=
which is undefined
x
0
uc
x
0
uc
cot(t) =
=
= 0
y
1
uc
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