Deriving a sine function with horizontal shift in degrees

80 Views Asked by At

The specific example is the derivative of $f(t)=6\sin(7.2(t-12.5)) + 9\sin(4.8(t-18.75))+15.5$

I have tried changing it to radians, or find the derivative in degrees. But all the explanations are beyond my maths level and therefore I cannot extrapolate them into a situation where it is not just a simple $\sin(x)$

Thank you in advance

1

There are 1 best solutions below

2
On

Hint:

For $f(x)=\sin(ax+b)$, the derivative $\mathrm dy/\mathrm dx$ can be calculated as follows:

$$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\mathrm dy}{\mathrm d(ax+b)}\cdot\dfrac{\mathrm d(ax+b)}{\mathrm dx}$$

Also note that the derivative is a linear operator. Define $\text{D}[f]$ as the derivative of $f$ wrt $x$, then $\text{D}[f\pm g]=\text{D}[f]\pm \text{D}[g]$.

Sure I would suggest changing it to radians to get a better graph. It gets easier viewing a sinusoid with input in radian measure.