Answer Sheet for Activity #4
Question #1:
This question is simply instructions to familiarize with the applet. Thus there is no solution to this problem.
Question #2:
This question is simply instructions on how to use the applet to create a graph. Thus there is no solution to this problem.
Question #3:
The purpose of this question is to have them reflect on why and how they made there graph. In other words, this question has the students focusing them to start thinking about key features of the graph such as the shape, zeros, intervals, any major points, etc. Thus the solution for this question is that there are multiple. In other words, there is no specific solution for this question since students will all have different reasons for why they made the graph the way they did.
Question #4:
The purpose of this question is to again have the students focusing on key features of the graph, and with the added feature of moving students towards how the unit circle will translate onto a graph. In other words, with this question students are starting to explore how the coordinates of the unit circle will look on the graph. Thus for this question, this requires students to put into practice what they have learned in the previous activities. Thus the solution for this question is going to require students to show how the point's path on the circle and the graph relate with each other through the use of intervals, angles (degrees and radians), zeros, etc.
Question #5:
The purpose of this question is to reiterate from the previous activity what the sine and cosine values represent in the coordinate plane. Through the investigations of the previous questions students can simply restate the fact. Thus the solution for this question is that the sine values represent the y-coordinates and the cosine values represent the x-coordinates of the unit circle.
Question #6:
The purpose of this question is for students to realize that the graph of the blue seat is actually a sine graph. For this students, can simply look at how the angle changes the coordinates of the blue point on the circle and comparing that to how the angle changes the coordinates of the blue seat function. Hopefully through this, they can see that the sine function is the best representation for this graph. Thus the solution would be that the sine function best represents the path of the blue seat because of this observation.
Question #7:
The purpose of this question is to have students to critique their previous made graphs with the knowledge they learned earlier about shape, zeros, intervals, key points, etc. With this, students can use the applet to show the graph of the blue seat function and compare that to the graph they drew. Then they can use this to explain why theirs was different or the similar to that of the actual function. Thus the solution to this question should be along the lines of my graph was different/similar because of this observation.
Question #8:
The purpose of this question is for students to focus on the key features that they observed with the sine and cosine graphs. With this students will be able to generalize or come up with the amplitude, period, and frequency of the graphs while also generalizing the shape, direction, zeros, and major points of the graph. Thus the solution would have to mention these qualities: the shape, zeros, intervals, and major points of both the sine and cosine graphs.
This question is simply instructions to familiarize with the applet. Thus there is no solution to this problem.
Question #2:
This question is simply instructions on how to use the applet to create a graph. Thus there is no solution to this problem.
Question #3:
The purpose of this question is to have them reflect on why and how they made there graph. In other words, this question has the students focusing them to start thinking about key features of the graph such as the shape, zeros, intervals, any major points, etc. Thus the solution for this question is that there are multiple. In other words, there is no specific solution for this question since students will all have different reasons for why they made the graph the way they did.
Question #4:
The purpose of this question is to again have the students focusing on key features of the graph, and with the added feature of moving students towards how the unit circle will translate onto a graph. In other words, with this question students are starting to explore how the coordinates of the unit circle will look on the graph. Thus for this question, this requires students to put into practice what they have learned in the previous activities. Thus the solution for this question is going to require students to show how the point's path on the circle and the graph relate with each other through the use of intervals, angles (degrees and radians), zeros, etc.
Question #5:
The purpose of this question is to reiterate from the previous activity what the sine and cosine values represent in the coordinate plane. Through the investigations of the previous questions students can simply restate the fact. Thus the solution for this question is that the sine values represent the y-coordinates and the cosine values represent the x-coordinates of the unit circle.
Question #6:
The purpose of this question is for students to realize that the graph of the blue seat is actually a sine graph. For this students, can simply look at how the angle changes the coordinates of the blue point on the circle and comparing that to how the angle changes the coordinates of the blue seat function. Hopefully through this, they can see that the sine function is the best representation for this graph. Thus the solution would be that the sine function best represents the path of the blue seat because of this observation.
Question #7:
The purpose of this question is to have students to critique their previous made graphs with the knowledge they learned earlier about shape, zeros, intervals, key points, etc. With this, students can use the applet to show the graph of the blue seat function and compare that to the graph they drew. Then they can use this to explain why theirs was different or the similar to that of the actual function. Thus the solution to this question should be along the lines of my graph was different/similar because of this observation.
Question #8:
The purpose of this question is for students to focus on the key features that they observed with the sine and cosine graphs. With this students will be able to generalize or come up with the amplitude, period, and frequency of the graphs while also generalizing the shape, direction, zeros, and major points of the graph. Thus the solution would have to mention these qualities: the shape, zeros, intervals, and major points of both the sine and cosine graphs.