Precalculus
"All The Mathematical Methods I Learned In My University Math Degree Became Obsolete In My Lifetime" - Keith Devlin
General graphing:
The following Desmos calculator demonstrates multiple ways in which
Desmos can be used to graph things, including lines (in multiple forms)
inequalities and non-linear functions. By graphing multiple lines
at once, one can also identify the solution to system of equation in 2
variables. Currently displayed below are lines y=2x-3 and 2x+2y=6
(the point satisfying both equations is (2,1)). Other graphs are
turned off, but you can click them off or on with buttons on the right:
(https://www.desmos.com/calculator/fhqvingjmw)
Quadratics: Quadtratic equations are typically expressed in standard form (y=ax^2+bc+x), vertex-form (y=a(x-h)^2+k). If you know the form of your quadratic, you can select the appropriate folder and see the grapj of the resulting parabola, as well as the other form of the quadratic: (https://www.desmos.com/calculator/pt0684s7ci)
Transformations: Here, we graph two functions. One is this funky piece-wise function f(x). Then, we have g(x), which is the transformation: g(x)=bf(ax+h)+k. By varying the parameters a,b,h,k, you can see how they transform the graph of g(x). https://www.desmos.com/calculator/tncircvzlg
Composition of functions: Enter f(x) and g(x) below, then the sage cell will display the composition f(g(x)):
Sin, Cos and Tan on the Unit Circle: We see that cos(t) and sin(t) are the x and y values on the unit circle, with angle t. As we drag t, we can see these values change, and graph their change. Moreover, we can see that Tan is the slope of the line induced by angle t: https://www.desmos.com/calculator/zw1ywfpvd3
All Trig functions: All six standard trignometric functions and their relation to each other. (https://www.desmos.com/calculator/kge1lueefh)
Angle Sum Identity: The Angle Sum Identity visualized. (https://www.desmos.com/calculator/lypgccsfhi)
Quadratics: Quadtratic equations are typically expressed in standard form (y=ax^2+bc+x), vertex-form (y=a(x-h)^2+k). If you know the form of your quadratic, you can select the appropriate folder and see the grapj of the resulting parabola, as well as the other form of the quadratic: (https://www.desmos.com/calculator/pt0684s7ci)
Transformations: Here, we graph two functions. One is this funky piece-wise function f(x). Then, we have g(x), which is the transformation: g(x)=bf(ax+h)+k. By varying the parameters a,b,h,k, you can see how they transform the graph of g(x). https://www.desmos.com/calculator/tncircvzlg
Composition of functions: Enter f(x) and g(x) below, then the sage cell will display the composition f(g(x)):
Sin, Cos and Tan on the Unit Circle: We see that cos(t) and sin(t) are the x and y values on the unit circle, with angle t. As we drag t, we can see these values change, and graph their change. Moreover, we can see that Tan is the slope of the line induced by angle t: https://www.desmos.com/calculator/zw1ywfpvd3
All Trig functions: All six standard trignometric functions and their relation to each other. (https://www.desmos.com/calculator/kge1lueefh)
Angle Sum Identity: The Angle Sum Identity visualized. (https://www.desmos.com/calculator/lypgccsfhi)