Examples of using Unit circle in English and their translations into Thai
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Colloquial
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Ecclesiastic
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Ecclesiastic
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Computer
This comes straight out of the unit circle definition: sine squared plus cosine squared, this is just equal to 1.
And so if where it intersects the unit circle is at 1 comma 0, then sine of theta is just the y-coordinate.
And so when we did it using the unit circle, we were able to get that answer.
I explained it in the unit circle video, and that's because the equation for the unit circle is x squared plus y squared is equal to 1.
That there is this relationship here there is this relationship between these trig functions and the unit circle, here between our newly defined hyperbolic trig functions and the unit hyperbola.
So let me draw at least the first and fourth quadrants of the unit circle.
Well, by definition, sine of x is defined to be the y-coordinate of any point on the unit circle.
Our new definition of the trig functions was that sine of theta is equal to the y-coordinate, right, this is y-coordinate where it intersects the unit circle.
So when theta's 0, right, then the radius between it-- this is the radius and this is the point where the radius intersects the unit circle.
Plus sine of pi/2, for the same reason, we're pointing straight up on the unit circle, so the y-coordinate, or the sine coordinate, is 1, right on the unit-- is essentially at the point 0, 1 on the unit circle.
And you would also find if you were to vary t it's going to trace out… just as if you were to vary t here it traces out the unit circle… if you trace t here it will trace out the right-hand side.
Tau radians means we have gone all the way around the unit circle, so cosine of tau- remember, we're back at the beginning of the unit circle right over here, so cosine of tau is going to be equal to 1 and then sine of tau is equal to 0.
And so its equation is the units circle.
It's going to be the top right of a circle, of the units circle.
And if we wanted to convert his, kind of, course angles into unit circles-- you know, with unit circles, you start here and you go all the way around this way.
Then think back to the unit circle.
So negative a, unit circle would look something.
Well, what's the area of this unit circle?
That's my best attempt at drawing the unit circle.
We intersect with unit circle at negative 1 comma 0.