Use the Exploration Guides to complete the following Interactivities:
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1. Sine Function
2. The Cosine Curve
3. The Tangent Curve
4. Translating and Scaling Sine and Cosine Functions
What have you learned from these "InterActivities" about the graphs of sine, cosine, and tangent functions?
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Be prepared for a quiz when this assignment is completed.
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15 years ago
12 comments:
All Algebra 2 MYP comments on the powers of i have been moved to the appropriate post.
From this assignment i have learned some important things that apply to graphing trigonometric functions. These include: how the unit circle relates to the graphs of either sine or cosine, what each of the variables stands for in a trigonometric equation, which way to translate sine and cosine graphs, how the cosine is the y-value on the unit circle, and how the x-value on the unit circle is the the sine value. I also learned how to work an apple computer(somewhat). I learned that a a tangent graph is infinite too.
5 Things that i have learned are that:
- in a sine equation, the value of h translates the graph left and right
- in a cosine equation, the value of k translates the graph up or down
- in a tangent equation, there are an infinite amount of graphs
- in a cosine equation in degrees, the period is 360 of the absolute value of b
- in a sine equation, the value of k translates the graph up and down
5 things I learned are:
The sine and cosine graphs are similar.
When you change K in those equations, the graph will move up or down
When b is changed, the graph's width increases and decreases.
When you change h, the graph shifts left and right, accordingly.
The tangent is the only graph of the 3 that has asymptotes.
-b affects the period of the graphs of trigonometric functions
-the graphs of sine and cosine are reflections of each other
-period can be determined with the formula 2pi/the absolute value of b
-trigonometric equations repeat each period over and over infinitely
-as b increases and decreases the frequency increases and the period decreases, but the amplitude does not change
I learned about the different ways that the unit circle interacts with the graph of trig functions. I also learned that the h translates the graph left or right and k translates the graph up and down. Tangent graphs are y over x and that they are infinite.
From this assignment i have learned an abudant amount of important things that apply to graphing trigonometrics functions.
-when viewing a cosine equation on a graph, the value of k determines the translation of the grpah, it may either translate up or down.
-out of sine, cosine, and tangent, a tangent graph is the only one that includes asymptotes.
-the graphs of sine and cosine are reflections of one another.
-the graph of y=sin(x) always passes through the origin
-lastly,i was able to revise and better understand how cosine is the y-value on the unit circle and how sine is the x-value on the unit circle.
Throughout this sine/cosine/tangent assignment, I have gathered a lot of information. Here are the top five.
-The tangent graph is the only graph to include asymptotes.
-The unit circle plays a major role in graphing trig functions, so i now see why teachers stress so much learn it.
-The value of k in the sine equation affects the graph in which it moves up along the y-axis for positive values or down for negative values.
-The tangent graph has infinitely many solutions.
-The graph of sine and cosine are similar (reflections of one another.)
The 5 things I learned from this assignment were:
1. What the Graphs for sine functions, cosine functions, and tangent functions look like.
2.What teh variables a, b, h and k stand for.
3. What happens to the graph and the unit circle when the value of Theta changes.
4.How to find the maximum and minimum of a graph using only the equation.
5. The ways the unit circle interacts and connects to graphing sine, and cosine functions.
I received a better understanding about graphing sine, cosine, and tangent functions. In the assignment I got:
- a better out look on the difference between graph's specific equation and it's parent graph.
- I understood how different the graphs look by varying the variables of "k","a", and "h".
_-I see the difference between the graphs of the function of sine, cosine, and tangent.
-I finally got the visual reason of why the x-coordinate represents cosine and y-coordinate represents sine.
-I figured out how to graph functions such as y=sinx,y=cosx, and y=tanx.
From this assignment, i have learned many things. some include...
-how the different graphs of sine,
cosine, and tangent equations look
-how the unit circle relates to
the graphs of these equaitons
-what each of the variables stands
for in each of the functions
-what effects occur from changing
the values of the variables
-the graphs of sine and cosine are
reflections of eachother
After doing this activity I learned:
• The period of a sin/cos function can be determined by using the formula 2π/|b|.
• There are infinitely many points in a tangent function.
• The graphs of sine and cosine have similar patterns.
• Tangent functions are the only functions that consist of asymptotes.
• The points on the unit circle have a direct relation with the points on the graphs of all trigonometric functions.
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