Examples of using Cosine of theta in English and their translations into Polish
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So what is the cosine of theta?
These cosine of theta divided by cosine of theta, that is equal to 1.
So our rate is s cosine of theta.
So we have the cosine of theta is equal to the adjacent,
We know that that is going to be s cosine of theta.
So in this case cosine of theta is equal to the adjacent side,
We know that's equal to y/r plus cosine of theta.
So we could say that the cosine of theta is equal to the adjacent side to the angle,
And this is the same thing as cosine of theta is equal to x/r.
Let's say that we have the polar coordinates r is equal to sine of theta plus cosine of theta.
So we get r sine of theta minus 2r cosine of theta is equal to minus 3.
That becomes the square root of cosine squared of theta, which is just the same thing as cosine of theta.
So, with that out of the way, we say that cosine of theta is equal to adjacent over the hypotenuse.
Divide both sides by this expression, so you're left with r is equal to minus 3 divided by sine of theta minus 2 cosine of theta.
This is equal to cosine of theta, that's just the derivative of sine of theta times our second expression. Times cosine of theta to the minus 1.
So we're ready to figure out what cosine of theta equals.
we could just write that dx is equal to square root of 3 over the square root of 2 cosine of theta d theta. .
And what's sine of theta divided by cosine of theta?
I have a cosine of theta divided by a cosine of theta, those cancel out, so we will just get 1,
The derivative of sine theta is cosine of theta.
And now divide both sides by this big expression, and you're left with r is equal to 10, 3 sine of theta-- 10 divided by 3 sine of theta minus 7 cosine of theta.
We know we know that cosine squared of theta is equal to 1 minus sine squared of theta, or that cosine of theta is equal to the square root of 1 minus sine squared of theta. .
And if you would actually just taken the principal roots at this stage of the equation, you would have gotten that the cosine of theta has to equal sine of theta over this interval, and that only happens at 45 degrees.
So the optimal distance that we are going to travel, so distance as a function-- the distance we travel at 45 degrees is going to be equal to 2s squared over g times cosine of theta, which is square root of 2 over 2.
which is equal to sine of theta cosine of theta plus, the thetas get swapped around, sine of theta plus cosine of theta, which is equal to, this is just the same thing written twice, 2 sine of theta cosine of theta.
so we get r times sine of theta minus 2 cosine of theta is equal to minus 3.
Well that's the same thing as sine of theta over cosine of theta squared.
So our integral becomes, so our integral is equal to, 2 times the square root of cosine squared of theta, so that's just 2 times cosine of theta, times 2 times cosine of theta.
2 sine of theta cosine of theta, and of course we have a plus c.