Cos

Cosh

Hyperbolic cosine

Arc cosine

It's cosine.

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

So I'm just going to write my cosine of t first.

Inverse hyperbolic cosine

Cosine to the fifth of x.

You would have thought that the cosecant is 1 over cosine.

Well the derivative of sine of x is just cosine of x. So it's going to be negative 2 cosine of x.

This is just what sine, cosine, and tangent are.

Hyperbolic cosine

That's the cosine of x.

Cosine of x becomes u.

So it's 5 cosine to the fourth of x.

It's cosine of x.

Cosine of x d of x.

Cosine of minus theta is equal to cosine of theta.

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

So the derivative of g of x is cosine of x.

It was the antiderivative of cosine of x.

Well, cosine is adjacent over hypotenuse.

So the convolution of sine of t with cosine of t is 1 2t sine of t.

So if u is equal to cosine of x, this thing is equal to 1 over cosine of x plus c is equal to the antiderivative of our original problem, which was sin of x over cosine of x squared dx.

And so that equals cosine of 2x over sine of 2x, right?

We're taking the convolution of sine of t with cosine of t.

So x sub 2, x sub 2 is going to be equal to its going to be equal to the cosine, the cos(2pi 3) i sin(2pi 3).

That will be equal to cosine of whatever is in front of the i, so cosine of mu x plus i sine of mu x.

Well, it's just cosine of x.

Again cosine is adjacent over hypotenuse

Well, yeah, it's just cosine of x.

All of that over cosine of x squared.

This means cosine of x to the fifth.

Soh cah toa, cos is adjacent over hypotenuse

What's cosine of 90 degrees?

What's the derivative of cosine of x?

And tangent is sine over cosine, so cotangent's the opposite.

Times cosine of minus mu x plus i sine of minus mu x.

Well, tangent is just sine over cosine.

And then we have minus cosine of t.

And the antiderivative of cosine of x is sine of x, which is just as complicated.

We could have solved for y in terms of x and we would have gotten the sine of the arccosine.

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

So it's cosine squared of tau, and then minus let's rewrite the cosine of t first, and I'm doing that because we're integrating with respect to tau.