Graphs of goniometric functions
Kapitoly: Basic goniometric functions, The unit circle, Cyclometric Arcus functions, Sine, cosine, tangent and cotangent, Formulas for goniometric functions, Graphs of goniometric functions, The sine and cosine theorem
Graphs of goniometric functions occur frequently and naturally in the wild. Here we will show what their basic form is and how they can change depending on the argument.
The graph of the sine function
The basic graph of the sine function looks like this:
What happens if we change the argument of the sine function? For example, if instead of the bare x, we insert 2x as an argument ? The answer is that if we decrease the period of the curve, it will "oscillate" faster. Conversely, if we put the expression x/2 as the argument to the function, the curve will become more elongated, the period will increase. This is clearly shown in the following figure, with the plain function sin(x) left in for emphasis.
If, on the other hand, you try to double the whole sin value, the curve will just be twice as high or twice as low at each point. Similarly, try dividing the resulting value by two. Again, to illustrate the picture:
Graph of the cosine function
The basic graph of the cosine function looks like this:
When the argument of the function is changed, the graph of cosine changes in a similar way to the graph of the sine function.
The graph will also change in exactly the same way if you multiply or divide the result by two:
The graph of the tangent function
The basic graph of the tangent function looks like this:
If we change the argument of the function to 2x, the period changes and the graph becomes narrower. Conversely, if we change the argument to x/2, the graph will be wider.
If we multiply the resulting value by two, the graph will be "flatter", if we divide by two, the graph will be more rounded.
