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Section 4.3 The Unit Circle. Quadrantal Angles. π 2. , 90˚. (0, 1). A. S. 0, 0˚ 2 π , 360˚. π , 180˚. (-1, 0). (1, 0). T. C. (0, -1). 3π 2. , 270˚. “ A ll S tudents T ake C alculus” tells you where each trig function is positive. Let’s begin with an easy family…. - PowerPoint PPT Presentation
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Section 4.3 The Unit Circle
(0, 1)
(0, -1)
(1, 0)(-1, 0)
0, 0˚ 2π, 360˚
π2
, 90˚
π, 180˚
3π 2
, 270˚
Quadrantal Angles
“All Students Take Calculus” tells you where each trig function is positive.
AS
T C
, 180 0, 02, 360
3
2
2
Let’s begin with an easy family… 4
2
2
2
2
1
45
2
2,
2
2
What are the coordinates?
4
Now, reflect the triangle to the second quadrant…
What are the coordinates?
, 180 0, 02, 360
3
2
2
2
2
2
2
1
45
2
2,
2
2
4
Now, reflect the triangle to the third quadrant…
1
-2
2
2
2
-2
2,
2
2 3
4
What are the coordinates?
Now, reflect the triangle to the fourth quadrant…
, 180 0, 02, 360
3
2
2
2
2
2
2
1
45
2
2,
2
2
4
1
-2
2
2
2
-2
2,
2
2 3
4
-2
2, -
2
2 5
4
What are the coordinates?
, 180 0, 02, 360
3
2
2
2
2
2
2
1
45
2
2,
2
2
4
1
-2
2
2
2
-2
2,
2
2 3
4
-2
2, -
2
2 5
4
2
2, -
2
2 7
4
EX. Evaluate the six trig functions at θ = .
**REMEMBER!!! cos θ is represented by the x-coordinates and sin θ is represented by the y-coordinates.**
4
EX. Evaluate the six trig functions at θ = .3
4
Homework: worksheet
30
1 1
2
3
2
6
3
2,1
2
Now, reflect the triangle to the second quadrant.
Complete the family… 6
30
1 1
2
3
2
6
3
2,1
2
Now, reflect the triangle to the third quadrant.
5
6
1
2
-3
2
-3
2,1
2
30
1 1
2
3
2
6
3
2,1
2
Now, reflect the triangle to the fourth quadrant.
5
61
2
-3
2
-3
2,1
2
-3
2, -
1
2
What are the coordinates?
7
6
What are the coordinates?
30
11
2
3
2
6
3
2,1
2 5
6
1
2
-3
2
-3
2,1
2
-3
2, -
1
2 7
6
3
2, -
1
2 11
6
EX. Evaluate the six trig functions at θ = .
6
EX. Evaluate the six trig functions at θ = .
Homework: worksheet
7
6
3
3
2
1
2
1
2,
3
2
3
1
, 180 0, 02, 360
3
2
2
Complete the family…
Now, reflect the triangle to the second quadrant.
60˚
1
, 180 0, 02, 360
3
2
2
60
3
2
1
2
1
2,
3
2
3
1
-1
2
What are the coordinates?
-1
2,
3
2 2
3
3
2
Now, reflect the triangle to the third quadrant.
1
, 180 0, 02, 360
3
2
2
60
3
2
1
2
1
2,
3
2
3
13
2
-1
2
-1
2,
3
2 2
3
What are the coordinates?
-1
2, -
3
2 4
3
Now, reflect the triangle to the fourth quadrant.
1
, 180 0, 02, 360
3
2
2
60
3
2
1
2
1
2,
3
2
3
13
2
-1
2
-1
2,
3
2 2
3
-1
2, -
3
2 4
3
1
2, -
3
2
What are the coordinates?
5
3
Shortcut to remember ordered pairs in quadrant 1
1 32 23 1
1) Parenthesis2) Fractions with denominator of 23)
4) Square roots
EX. Evaluate the six trig functions at θ = .
3
EX. Evaluate the six trig functions at θ = .
Homework: worksheet
2
3
