How do you map sine functions to sine curves?
(2 votes)
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Without knowing the exact task, the question is not fully answered.
But if you set the following function:
A*sin(b*x+c) can be assigned the sine function to a drawing via the parameters a b and c
A changes the amplitude, i.e. the maximum value, of the sine curve
B thus changes the frequency, so to speak, the distance of the zero points
C changes the phase shift
If I remember it correctly, the sinus curve went through the coordinate line jump, so that c shifts the curve by the value from c to the right.
Does that help?
In this form, b would be the frequency, but the phase shift, which would be read from the sketch, would not correspond to c but c/b, because in your writing the changed frequency would already be calculated with the phase shift. Better use this form:
y = sin(b•(x+c))
Functions are assigned curves by marking each curve with the function it represents. At sin(x) the curve goes upwards through the zero point, at sin(x-PI) it goes downwards through the zero point, at sin(x-PI/2) it has a maximum in +1 at the zero point and at sin(x+PI/2) it has a minimum at the zero point (−1).
But I won’t let go of the suspicion that you want to know something completely different and you didn’t manage to express yourself understandably.
If the prefactor of the argument increases, then the frequency of the waves increases; if a constant is added to x, then the entire graph is shifted to the left by this value; increases the prefactor of the sine value, then the amplitude of the waves becomes greater and a constant is added to the sine value, then the entire function is shifted upward by this value.