# sine and cosine graphs

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```					    Unit 2 – Circular Functions
Lesson 7 – sine and cosine graphs
Unit 2 – Circular Functions
Lesson 7 – sine and cosine graphs

θ      0   π/6   π/3   π/2   2π/3   5π/6   π   7π/6   4π/3   3π/2   5π/3   11π/6

sin θ

Make dots!
Unit 2 – Circular Functions
Lesson 7 – sine and cosine graphs

θ      0   π/6   π/3   π/2   2π/3   5π/6   π   7π/6   4π/3   3π/2   5π/3   11π/6

cos θ

Make dots!
Unit 2 – Circular Functions
Lesson 7 – sine and cosine graphs

Properties of the sine graph:

1. Domain: all real numbers (wrapping function)
2. Range: [-1,1]
3. Y-Intercept: 0
4. Zeros: All integral multiples of π {kπ | k I}
5. Period: 2π
Unit 2 – Circular Functions
Lesson 7 – sine and cosine graphs

Properties of the sine graph:

6. Odd/Even?: odd (symmetrical in the origin)
7. Amplitude: 1 ([max. y – min. y]/2)
Unit 2 – Circular Functions
Lesson 7 – sine and cosine graphs

Properties of the sine graph:

8. Since the curve is above the axis in Quadrants I and
II, it follows that sin θ > 0 in these two quadrants.
Similarly, sin θ < 0 in quadrants III and IV.
9. As you move on the curve from left to right, the curve
is increasing in Quadrants I and IV and decreasing in
Sketch the cosine graph and record the 9 properties of the cosine graph:

1. Domain:
2. Range:
3. Y-Intercept:
4. Zeros:
5. Period:
6. Odd/Even?:
7. Amplitude:
8. Since the curve is…
9. As you move on the curve from left to right, the curve is…
Do Exercise 6:
#1-5, 9

```
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