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
Quadrants II and III.
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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posted:10/30/2012
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