Ferris Wheel Activity Student Instructions: Today we are going to start our unit on trigonometry with a Ferris wheel activity. This Ferris wheel will be used throughout the unit. Be sure to hold on to this Ferris wheel for the rest of the unit as it will help us generate different information necessary to be successful in trig. Before starting each activity, please read all the instruction first. There are times when you will glue and cut and you should make sure you understand all instructions before you begin. Activity 1 The Ferris Wheel 1. Go to the page labeled Unit Circle. Paste the unit circle on a piece of card stock. Cut out the circle but be careful as you cut out the circle to make sure that the dots around the circumference of the circle are still visible. 2. Go to the page labeled Cartesian plane with Unit Circle and cut out the Cartesian plane. Do not cut out the circle, cut out the graph paper square containing the circle. 3. Glue the graph paper on the top left position of the file folder (this is important to conserve space). 4. Poke a hole through the center of the cut out unit circle and the circle on the graph paper. 5. Push the brad clip through the center of both. This should create a disk that spins or you Ferris wheel Activity 2 Distance around the Unit Circle This circle has a radius of unit 1. Use this information to label the outside of the circle as follows: 1. Mark the outside of your Cartesian plane circle with the same marks that are on the Ferris wheel circle 2. You task is to enter the Ferris wheel at the 3:00 position and travel around the circle in a counterclockwise direction. You will stop the Ferris wheel at each marked position 3. Once you stop at a location, calculate the distance traveled along the circle from where you entered the Ferris wheel to your current location. 4. Label the circle with the degree measurement and length around the circle you have traveled at each location. Make sure you put your values on the outside of the circle at the place you stopped. 5. Leave your answers with π in the solution and in the numerator. 6. All fractions MUST be reduced. ****You must enter your Ferris Wheel from the right side at 3:00**** Activity 3 1. Mark the location of 1 radian on the outside of the circle. 2. Wait to discuss location with the class. 3. Now mark 2 6 radians on your wheel 4. How many radians fit around the circle? Activity 4 1. Use your knowledge of right angle trig and label the coordinates at each mark for your special angles. 2. Be careful that you consider which quadrant you point is located when determining the sign of your coordinate values. Activity 5 Generate scatter plots. 1. Find the value for each function given each angle measurement and fill in the Function Value Table. 2. Use the information to create three scatter plots on the coordinate graph paper. 3. The first one will have the input value radians and output value of sinθ. 4. The second will have the input value radians and output value of cosθ. 5. The third will have the input value radias and output value of tanθ.
6. Connect the dots on the scatter plot to form smooth curves. Create these scatter plots twice, one on each graph, for each function**** Activity 6 1. Glue the table below your Ferris wheel 2. On the other side glue down the three different scatter plots on the coordinate plane. Glue the graphs as close to the fold line as possible. Another set of graphs will be going to the right of these graphs. 3. Glue such that you are able to lift the graph so that you can see under it. Another graph will go here at a later date. 4. Label each graph with its name, domain, range, period, midline, and amplitude Activity 7 Reciprocal Graphs 1. Generate the reciprocal values in the table for secant, cosecant, and cotangent. 2. Use the generated a scatter plot graph for secθ, cscθ, and cotθ 3. Connect the dots on the scatter plot to form smooth curves (be careful about division by zero) 4. Glue the graph next to their reciprocal graph on the foldable 5. Label each graph with its name, domain, range, period, and asymptotes
. UNIT CIRCLE
Unit Circle on a Cartesian Plane 1 y f(x)=(1-x^2)^(1/2) f(x)=-(1-x^2)^(1/2) 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1-1 -0.9-0.8-0.7-0.6-0.5-0.4-0.3-0.2-0.1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-0.1 x -0.2-0.3-0.4-0.5-0.6-0.7-0.8-0.9-1
Function Value Table Degrees Radians sin θ cos θ tan θ csc θ sec θ cot θ O 30 45 60 90 120 135 150 180 210 225 240 270 300 315 330 360
Coordinate Plan graph paper