For a really clear plotter showing the connection between the Cartesian graph of r=f(θ) and the graph in polar coordinates try this Polar Curves and Cartesian Graphs applet. Watch the display carefully as you move the slider; you can easily see when r is negative for example.
For more on Polar Curves – including notes and the use of Desmos, see this post.
The best graphing calculator around is free and available on Android, get it on Google play here and is also available for Apple devices – iOS apps.
Desmos on Android has had a major upgrade and you can now access your account with all your saved graphs and also create new graphs. Press the three lines in the top left corner to sign in, sync up, and take all of your graphs on the go.
Tons of examples
Also included in this update:
* implicit inequalities
* draggable table columns
* a ton of new example graphs
* bugfixes and performance improvements
Maths students everywhere get this app! It’s great for younger students as it is easy to use for learning about graphs but has the sophisticated features that older students need.
From simple linear graphs to polar or parametric curves – Desmos does it all! ……
There are several examples in the slideshows here to show you the syntax you need on Desmos if you are unfamiliar with it and a series of pages giving you more information.
You can use the Desmos graphing calculator to support your study and understanding of functions. Using function notation you can enter composite functions as shown in the next two illustrations. Selecting each image will take you to the relevant Desmos graph page.
Composite Functions with Desmos – select image
Composite functions with Desmos – select image
For further exploration of composite functions check the pages in this slideshow.
You can also easily explore transformations of graphs with Desmos.
The best graphing calculator around is now available on Android (free). Get it on Google play here. (Desmos iOS apps have been available for some time).
Maths students everywhere get this app! It’s great for younger students as it is easy to use for learning about graphs but has the sophisticated features that older students need. From simple linear graphs to polar or parametric curves – Desmos does it all!
There are several examples in the slideshows here to show you the syntax you need on Desmos if you are unfamiliar with it.
Use the excellent Desmos graphing calculator to explore the gradient of a straight line. Select the image then you can change the sliders for m and c to change the line and drag the points so you can verify the gradient of the line.
If you are feeling a little unsure on identifying the equation of a straight line then use this Desmos graph and experiment by changing the gradient, intercept or points marked on the line. The image above shows the line y=2x+1. We can see that the intercept is 1 (where the line crosses the y axis) and the gradient is 2. Looking at the graph we can see that the gradient is positive and you can verify that the gradient is 2 by dividing the difference between the y coordinates (6 in this image) by the difference in the x coordinates (3 in this image). Try moving the points, you will see that this ratio remains constant.
Compare the second image. We can see that the intercept is 1. Looking at the slope, the gradient is positive. The gradient is given by 2÷4 = 0.5. So the equation of the line is y = 0.5x + 1.
In the third example; looking at the slope of the line we can see it is negative. The gradient is given by 6÷2 which is 3 and the line crosses the y axis at 2 giving the equation of the line as y = ─3x + 2
Since writing this post Desmos have taken the page and created a superior version!