And the sine function tells us that sine of theta actually,

Function to calculate the sine of a given angle

So you know, if the function if the derivative of a function is cosine, then we know the function itself is sine.

So let's say that I have the second derivative of my function y plus 4 times my function y is equal to sine of t minus the unit step function 0 up until 2 pi of t times sine of t minus 2 pi.

The anti derivative of this function is once again just e to the x and then f times that function unchanged time sine of x.

It's the integral from 0 to t, of sine of the first function of t minus tau.

So this is going to be minus 1 3 times the unit step function, where c is 2 pi of t times instead of sine of t sine of t minus 2pi.

This sine times this sine is sine squared of t cosine of t.

Sine

Sine

Sine

Plus the magnitude of the y component, which is r sine of theta, which is going to be a function of time.

So the derivative of sine with respect to theta, we're just doing the chain rule here, the derivative of sine with respect to theta is going to be cosine of theta as a function of t.

That's equal to sine over cosine divided by sine.

Horizontal Sine

Hyperbolic sine

Arc sine

So why not use sine? Sine is opposite over hypotenuse

Laplace Transform of sine of t plus sine of t.

Cosine derivative is minus sine, so minus B sine of x.

So sine of x d x, it's minus sine of x.

If you distribute the r, you get exactly r cosine theta as a function of t times our i unit vector plus our sine theta as a function of t times the j unit vector.

Hyperbolic arc sine

Inverse hyperbolic sine

The way I often do it in my head, I see the sine of tau, cosine of tau. if I have a function and I have its derivative, I can treat that function just like as if I had an x there, so it'd be sine squared of tau over 2, which is exactly what we have there.

Sine of 2x is equal to 2 sine of x cosine of x.

What function, when I take its second and first derivatives and add and subtract multiples of them to each other, will I get sine of x?

Sine qua non ( ) or condicio sine qua non (plural condiciones sine quibus non ) refers to an indispensable and essential action, condition, or ingredient.

Plus this very last term, which is 1 6 times the unit step function 2 pi of t, the unit step function that steps up at 2 pi times sine of and we have to be careful here.

Times sine of x.

sine of theta t

Sine is 0, 0.

What's sine of infinity?

Sine of 2 pi.

It's 1 over sine.

I'm doing is I'm taking the absolute value of sine of x, absolute value of sine of x, absolute value of sine of x.

And when t is pi, sine of pi that's sine of 180 degrees that's 0.

And if this was sine of 2x, I'd put A times sine of 2x here.

I take the derivative of sine c squared and I get 2 sine of c,

Sine of 0 is 0.

Sine is opposite over hypotenuse.

2 times s sine theta.

Well, it's sine of x.

So that's sine of x.

It's sine of alpha t.