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ok so what do we know about the unit circle?

the radius=1, remember this, we're gonna need it later

Ok first draw the unit circle. Draw and X and Y access, and at the points (0,1) (1,0) (-1,0) (0,-1) draw dots, and connect the dots with your best attempt at a circle. Basically what you want to do now is draw an arbitrary radius in your unit circle somewhere around 45 degrees. (draw the line x=y where both x and y are positive)

So here's the part were I make some sort of guess of what you've learned prior to this.

Ok here's what you should know, the name of the Indian princess SohCahToa.

Which is really an clever way to help you remember sin(t)=opposite/hypotenuse, cos(t)=adjacent/hypotenuse, and tan(t)=opposite/adjacent.

What you just did when you drew the 45 degree line is you created a triangle between your x-axis, and your radius line. Its a triangle with hypotenuse = 1, because the radius is 1. Lets just call the height 'Y', since the height goes up and down along the y axis, depending on the angle. And lets call the width 'X' since it shrinks or grows along the x axis based on how far up the line is pointing.

Now lets use the formulas with respect to that 45-ish degree angle

sin=opposite/hypotenuse, so that's just the height/hypotenuse = Y/1 = Y

so sin(t)=Y

cos=adjacent/hypotenuse, so that's the width/hypotenuse = X/1 = 1

so cos(t)=X

and your done

but just because we can, lets do the tan,

tan=opposite/adjacent, so that's the height/width - Y/X

any questions?