do now: graph the equation: x 2 + y 2 = 1 draw and label the special right triangles what happens...
TRANSCRIPT
![Page 1: Do Now: Graph the equation: X 2 + y 2 = 1 Draw and label the special right triangles What happens when the hypotenuse of each triangle equals 1?](https://reader035.vdocument.in/reader035/viewer/2022070401/56649f185503460f94c2f3be/html5/thumbnails/1.jpg)
Do Now:
• Graph the equation:
X2 + y2 = 1
• Draw and label the special right triangles• What happens when the hypotenuse of each
triangle equals 1?
![Page 2: Do Now: Graph the equation: X 2 + y 2 = 1 Draw and label the special right triangles What happens when the hypotenuse of each triangle equals 1?](https://reader035.vdocument.in/reader035/viewer/2022070401/56649f185503460f94c2f3be/html5/thumbnails/2.jpg)
PRE-CALC: 4.2: TRIG FUNCTIONS: THE UNIT CIRCLE
ALGEBRA II HONORS
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Trigonometry
• The word trigonometry means measurement of triangles.
• Initially trigonometry dealt with the relationships among the sides and angles of triangles.
y
x
x
y
r
x
r
y
)tan(
)cos(
)sin(
r
![Page 4: Do Now: Graph the equation: X 2 + y 2 = 1 Draw and label the special right triangles What happens when the hypotenuse of each triangle equals 1?](https://reader035.vdocument.in/reader035/viewer/2022070401/56649f185503460f94c2f3be/html5/thumbnails/4.jpg)
Trigonometry
y
x
y
x
x
y
x
r
r
x
r
y
)cot( )tan(
)sec( )cos(
y
r)csc( )sin(
r
![Page 5: Do Now: Graph the equation: X 2 + y 2 = 1 Draw and label the special right triangles What happens when the hypotenuse of each triangle equals 1?](https://reader035.vdocument.in/reader035/viewer/2022070401/56649f185503460f94c2f3be/html5/thumbnails/5.jpg)
SIX TRIGONOMETRIC FUNCTIONS
• Sine (sin)• Cosine (cos)• Tangent (tan)• Cosecant (csc)• Secant (sec)• Cotangent (cot)
![Page 6: Do Now: Graph the equation: X 2 + y 2 = 1 Draw and label the special right triangles What happens when the hypotenuse of each triangle equals 1?](https://reader035.vdocument.in/reader035/viewer/2022070401/56649f185503460f94c2f3be/html5/thumbnails/6.jpg)
UNIT CIRCLE: X2 + Y2 = 1
(1,0)
(0,1)
(0,-1)
(-1,0)
![Page 7: Do Now: Graph the equation: X 2 + y 2 = 1 Draw and label the special right triangles What happens when the hypotenuse of each triangle equals 1?](https://reader035.vdocument.in/reader035/viewer/2022070401/56649f185503460f94c2f3be/html5/thumbnails/7.jpg)
UNIT CIRCLE: X2 + Y2 = 1
x
yr
(x,y)
(0,1)
(1,0)
(0,-1)
(-1,0)
![Page 8: Do Now: Graph the equation: X 2 + y 2 = 1 Draw and label the special right triangles What happens when the hypotenuse of each triangle equals 1?](https://reader035.vdocument.in/reader035/viewer/2022070401/56649f185503460f94c2f3be/html5/thumbnails/8.jpg)
UNIT CIRCLE: X2 + Y2 = 1
x
y1
(x,y)
(0,1)
(1,0)
(0,-1)
(-1,0)
![Page 9: Do Now: Graph the equation: X 2 + y 2 = 1 Draw and label the special right triangles What happens when the hypotenuse of each triangle equals 1?](https://reader035.vdocument.in/reader035/viewer/2022070401/56649f185503460f94c2f3be/html5/thumbnails/9.jpg)
Unit Circle Trig
y
x
y
x
x
y
x
x
y
)cot( )tan(
1)sec(
1)cos(
y
1)csc(
1)sin(
1
![Page 10: Do Now: Graph the equation: X 2 + y 2 = 1 Draw and label the special right triangles What happens when the hypotenuse of each triangle equals 1?](https://reader035.vdocument.in/reader035/viewer/2022070401/56649f185503460f94c2f3be/html5/thumbnails/10.jpg)
UNIT CIRCLE: X2 + Y2 = 1
1)sin,(cos
cos
sin
(0,1)
(1,0)
(0,-1)
(-1,0)
![Page 11: Do Now: Graph the equation: X 2 + y 2 = 1 Draw and label the special right triangles What happens when the hypotenuse of each triangle equals 1?](https://reader035.vdocument.in/reader035/viewer/2022070401/56649f185503460f94c2f3be/html5/thumbnails/11.jpg)
UNIT CIRCLE
• Let the radius = 1.• Graph x2 + y2 = 1• Find the (x, y)
coordinates using special right triangle ratios for 45-45-90.
(1,0)
(0,1)
(-1,0)
(0,-1)
![Page 12: Do Now: Graph the equation: X 2 + y 2 = 1 Draw and label the special right triangles What happens when the hypotenuse of each triangle equals 1?](https://reader035.vdocument.in/reader035/viewer/2022070401/56649f185503460f94c2f3be/html5/thumbnails/12.jpg)
UNIT CIRCLE
• Find all the (x, y) coordinates using special right triangle ratios for 45-45-90.
(1,0)
(0,1)
(-1,0)
(0,-1)
![Page 13: Do Now: Graph the equation: X 2 + y 2 = 1 Draw and label the special right triangles What happens when the hypotenuse of each triangle equals 1?](https://reader035.vdocument.in/reader035/viewer/2022070401/56649f185503460f94c2f3be/html5/thumbnails/13.jpg)
UNIT CIRCLE
• Let the radius = 1.
• Find the (x, y) coordinates using special right triangle ratios for 30-60-90.
(1,0)
(0,1)
(-1,0)
(0,-1)
![Page 14: Do Now: Graph the equation: X 2 + y 2 = 1 Draw and label the special right triangles What happens when the hypotenuse of each triangle equals 1?](https://reader035.vdocument.in/reader035/viewer/2022070401/56649f185503460f94c2f3be/html5/thumbnails/14.jpg)
UNIT CIRCLE
• Let the radius = 1.
• Find the (x, y) coordinates using special right triangle ratios for 30-60-90.
(1,0)
(0,1)
(-1,0)
(0,-1)
![Page 15: Do Now: Graph the equation: X 2 + y 2 = 1 Draw and label the special right triangles What happens when the hypotenuse of each triangle equals 1?](https://reader035.vdocument.in/reader035/viewer/2022070401/56649f185503460f94c2f3be/html5/thumbnails/15.jpg)
UNIT CIRCLE
• Let the radius = 1.
• Find the (x, y) coordinates using special right triangle ratios for 30-60-90.
(1,0)
(0,1)
(-1,0)
(0,-1)
![Page 16: Do Now: Graph the equation: X 2 + y 2 = 1 Draw and label the special right triangles What happens when the hypotenuse of each triangle equals 1?](https://reader035.vdocument.in/reader035/viewer/2022070401/56649f185503460f94c2f3be/html5/thumbnails/16.jpg)
UNIT CIRCLE
• Let the radius = 1.
• Find the (x, y) coordinates using special right triangle ratios for 30-60-90.
(1,0)
(0,1)
(-1,0)
(0,-1)
![Page 17: Do Now: Graph the equation: X 2 + y 2 = 1 Draw and label the special right triangles What happens when the hypotenuse of each triangle equals 1?](https://reader035.vdocument.in/reader035/viewer/2022070401/56649f185503460f94c2f3be/html5/thumbnails/17.jpg)
UNIT CIRCLE: FOR EACH POINT ON THE UNIT CIRCLE LABEL THE ORDERED PAIR (COS, SIN) AND THE ANGLE IN DEGREES AND RADIANS.
![Page 18: Do Now: Graph the equation: X 2 + y 2 = 1 Draw and label the special right triangles What happens when the hypotenuse of each triangle equals 1?](https://reader035.vdocument.in/reader035/viewer/2022070401/56649f185503460f94c2f3be/html5/thumbnails/18.jpg)
Closing:
• What special triangles did we use to help us learn the unit circle?
![Page 19: Do Now: Graph the equation: X 2 + y 2 = 1 Draw and label the special right triangles What happens when the hypotenuse of each triangle equals 1?](https://reader035.vdocument.in/reader035/viewer/2022070401/56649f185503460f94c2f3be/html5/thumbnails/19.jpg)
Homework:
• worksheet
![Page 20: Do Now: Graph the equation: X 2 + y 2 = 1 Draw and label the special right triangles What happens when the hypotenuse of each triangle equals 1?](https://reader035.vdocument.in/reader035/viewer/2022070401/56649f185503460f94c2f3be/html5/thumbnails/20.jpg)
DO NOW: FOR EACH POINT ON THE UNIT CIRCLE LABEL THE ORDERED PAIR (COS, SIN) AND THE ANGLE IN DEGREES AND RADIANS.
![Page 21: Do Now: Graph the equation: X 2 + y 2 = 1 Draw and label the special right triangles What happens when the hypotenuse of each triangle equals 1?](https://reader035.vdocument.in/reader035/viewer/2022070401/56649f185503460f94c2f3be/html5/thumbnails/21.jpg)
UNIT CIRCLE WORKSHEET radians degrees cos sin tan sec csc cot 1. 0
2.
6
3.
4
4.
3
5.
2
6.
3
2
7.
4
3
8.
6
5
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UNIT CIRCLE WORKSHEET9.
10.
6
7
11.
4
5
12.
3
4
13.
2
3
14.
3
5
15.
4
7
16.
6
11
17. 2
radians degrees cos sin tan sec csc cot
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Practice
![Page 24: Do Now: Graph the equation: X 2 + y 2 = 1 Draw and label the special right triangles What happens when the hypotenuse of each triangle equals 1?](https://reader035.vdocument.in/reader035/viewer/2022070401/56649f185503460f94c2f3be/html5/thumbnails/24.jpg)
Practice
![Page 25: Do Now: Graph the equation: X 2 + y 2 = 1 Draw and label the special right triangles What happens when the hypotenuse of each triangle equals 1?](https://reader035.vdocument.in/reader035/viewer/2022070401/56649f185503460f94c2f3be/html5/thumbnails/25.jpg)
Practice
![Page 26: Do Now: Graph the equation: X 2 + y 2 = 1 Draw and label the special right triangles What happens when the hypotenuse of each triangle equals 1?](https://reader035.vdocument.in/reader035/viewer/2022070401/56649f185503460f94c2f3be/html5/thumbnails/26.jpg)
Trigonometry
y
x
y
x
x
y
x
x
y
)cot( )tan(
1)sec(
1)cos(
y
1)csc(
1)sin(
1
![Page 27: Do Now: Graph the equation: X 2 + y 2 = 1 Draw and label the special right triangles What happens when the hypotenuse of each triangle equals 1?](https://reader035.vdocument.in/reader035/viewer/2022070401/56649f185503460f94c2f3be/html5/thumbnails/27.jpg)
Trigonometry:
•Given that cos = x and sin = y •Find a new way to write tan, cot, sec, and csc.
![Page 28: Do Now: Graph the equation: X 2 + y 2 = 1 Draw and label the special right triangles What happens when the hypotenuse of each triangle equals 1?](https://reader035.vdocument.in/reader035/viewer/2022070401/56649f185503460f94c2f3be/html5/thumbnails/28.jpg)
TRIG FUNCTIONS: UNIT CIRCLE
(reciprocal of cosine)
cos
sintan
cos
1sec
sin
1csc (reciprocal of sine)
sin
coscot
![Page 29: Do Now: Graph the equation: X 2 + y 2 = 1 Draw and label the special right triangles What happens when the hypotenuse of each triangle equals 1?](https://reader035.vdocument.in/reader035/viewer/2022070401/56649f185503460f94c2f3be/html5/thumbnails/29.jpg)
Practice
![Page 30: Do Now: Graph the equation: X 2 + y 2 = 1 Draw and label the special right triangles What happens when the hypotenuse of each triangle equals 1?](https://reader035.vdocument.in/reader035/viewer/2022070401/56649f185503460f94c2f3be/html5/thumbnails/30.jpg)
Homework:
• Packet • 1-28