1. The Unit Circle & Trig Ratios
B. Afghani
Algebra PP2.ppt
The Unit Circle
& Trig Ratios
LBUSD Math Office, 2002

2. Today’s Learning Questions:
How do I create a unit circle?
What are the “special angles” and how do I graph their arcs & triangles?
How do I derive the side lengths for isosceles triangles whose hypotenuse = 1?

3. Today’s Learning Questions:
How do I derive the side lengths for triangles whose hypotenuse = 1?
What 5 values and their opposites are the sine and cosine values for each special angle between 0° and 360°?
How may I use the unit circle graph to find the sine of a special angle? The cosine of an angle?

4. Today’s Learning Bonus Question:
Why is the ratio of sine θ to cosine θ called tangent θ?

5. Angles Mathematicians Like
Solve for a.
45° 1 a
45° a

6. Angles Mathematicians Like
Solve for a. a 1 1 b
60° a a
60° 1

7. Angles Mathematicians Like
Solve for b. a 1 1 b
60° a a
60° 1

8. Put in order from least to greatest:

9. Please label these items on your coordinate grid:
The origin
The x-axis
The y-axis

10. What makes a circle a “unit circle”?
y-axis
r = 1
(0, 0)
the origin
What makes a circle a “unit circle”?
x-axis

11. (0, 1)
What are the coordinates for the graphed points? y
(1, 0)
(-1, 0) x
(0, -1)

12. y 1 y  x x

13. Trigonometric Ratios

14. 90° y
90°
120°
60°
45°
135°
150°
45°
30° a 1
0°, 360°
0°, 360°
180°
180° 0° 0°
45° x
210°
330°
225°
315°
240°
270°
270°
300°

15. y 0, x

16. 90° y
90°
120°
60°
45°
135°
150°
45°
30° a 1
0°, 360°
0°, 360°
180°
180° 0° 0°
45° x
210°
330°
225°
315°
240°
270°
270°
300°

17. Trig Ratios

18. y
90°
120°
60°
150°
30°
180°
0°, 360° 0° x
210°
330°
240°
270°
300°

19. y 0, x

20. Trig Ratios
60°
300°

21. Today’s Learning Questions:
How do I create a unit circle?
What are the “special angles” and how do I graph their arcs & triangles?
How do I derive the side lengths for isosceles triangles whose hypotenuse = 1?

22. Today’s Learning Questions:
How do I derive the side lengths for triangles whose hypotenuse = 1?
What 5 values and their opposites are the sine and cosine values for each special angle between 0° and 360°?
How may I use the unit circle graph to find the sine of a special angle? The cosine of an angle?

23. Today’s Learning Bonus Question:
Why is the ratio of sine θ to cosine θ called tangent θ?

24. Bonus Question