Examples of using Tangent of theta in English and their translations into Swedish
{-}
-
Colloquial
-
Official
-
Medicine
-
Ecclesiastic
-
Ecclesiastic
-
Official/political
-
Computer
-
Programming
-
Political
And then you have the tangent of theta.
The tangent of theta: opposite over adjacent.
This is the same thing as the inverse tan of the tangent of theta.
Oh, am I taking the whole tangent of theta to the negative power or something?
Tangent of theta is equal to the opposite-- which is y-- over the adjacent-- which is x.
You could write it as the arctan of the tangent of theta is equal to the arctan of 4/3.
It's going to be 6 times the derivative with respect to theta of tangent of theta.
So the derivative of tangent of theta is equal to secant squared of theta. .
We learned that sine of theta over cosine of theta is equal to tangent of theta.
Oh, what's tangent of x, tangent of theta." let's make it a little bit more concrete.
So that just says sine of theta over cosine of theta is equal to tangent of theta.
So if i ask you the tangent of- the tangent of theta once again go back to"soh cah toa.
the cosine of theta, and what the tangent of theta are.
So tangent of theta is equal to the opposite-- which is really the y-coordinate, which is equal to 4-- over the adjacent.
and then the tangent of theta is equal to opposite over adjacent.
The derivative of tangent of theta, that's the same thing as d d theta of sine of theta over cosine of theta. .
if we say let's make this thing right here equal to tangent of theta, or tangent squared of theta. .
And then, of course, you can-- in case I haven't done it already, you now know that sine of theta over cosine of theta is equal to tangent of theta.
you get x over 6 is equal to the tangent of theta, or that x is equal to 6 tangent of theta.
If we take the derivative of both sides of this with respect to theta we get d x d theta is equal to-- what's the derivative of the tangent of theta?
What's 1 plus tangent squared of theta?
Which is equal to 1 plus tangent squared of theta.
Then this expression will be 1 plus tangent squared of theta.
which is 36 times 1 plus tangent squared of theta.
We're going to say that x squared over 36 is equal to tangent squared of theta.
is 1 plus tangent squared of theta.
We learned that the tangent squared of theta plus 1 is equal to the secant of theta.
Tangent squared of theta, this is equal to 1 plus just the definition of tangent sine squared of theta over cosine squared of theta.
So the derivative of tangent theta-- never hurts to do it on the side, let me do it right here.