Trig­­Unit_Circle_Big_Picture.notebook
January 29, 2015
(Unit Circle Test Tomorrow)
Trig Warm­Up: Which is greater...
a) Cos ­7 or b) Cos 11 12
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(0, 1)
(1, 0)
(­1, 0)
(0, ­1)
37) Sin(t) =1/3
a) sin(­t) =
b) csc(­t)=
38) Cos(t)= ­3/4
a) cos (­t) = b) sec (­t) =
Jan 30­11:53 AM
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Trig­­Unit_Circle_Big_Picture.notebook
January 29, 2015
Homework?????
Jan 30­11:53 AM
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Trig­­Unit_Circle_Big_Picture.notebook
January 29, 2015
̵ ǤǤǤ
Things to think about...
1. What does T represent?
2. What does the x­value represent?
3. What does the y­value represent?
Jan 30­11:41 AM
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Trig­­Unit_Circle_Big_Picture.notebook
January 29, 2015
Exploring the Unit Circle...
Do you see the BIG Picture???
1. For any t, the value of the cos(t) lies between -1 and 1 inclusive.
2. For any t, the value of the sin(t) lies between -1 and 1 inclusive.
3. The values of cos(t) and cos(-t) are always equal to each other.
4. The values of sin(t) and sin(-t) are always equal to each other.
5. The values of sin(t) and sin(t + 2 ) are always equal to each other.
In fact, that is true for all 6 trig functions on their domains.
6. The values of sin(t) and sin(t + ) are always opposite of each other.
The same is true for cos(t) and cos(t + ).
7. The values of tan(t) and tan(t + ) are always equal to each other,
unless they are both undefined.
8. The sum (cos t)2 + (sin t)2 = 1.
cos ­
cos +
sin +
sin +
tan ­
tan +
cos ­
cos +
sin ­
sin ­
tan +
tan ­
Jan 30­11:54 AM
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Trig­­Unit_Circle_Big_Picture.notebook
January 29, 2015
More BIG PICTURE Unit Circle understanding...
1. Identify an angle, 0, such that cos 0 < 0 AND cot 0 > 0.
2. Identify an angle, 0, such that sin 0 > 0 AND sec 0 > 0.
3. Which is greater?????
a. sin 170 degrees or sin 190 degrees
b. sec 110 degrees or sec 150 degrees
c. tan 200 degrees or tan 210 degrees
d. cos 110 degrees or cos 150 degrees
Jan 30­11:54 AM
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Trig­­Unit_Circle_Big_Picture.notebook
January 29, 2015
* Degrees
* Radians
* (x, y) locations
Apr 28­11:07 AM
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