(a)x2+y2=1
This is the equation of unit circle,where radius equals 1.
Let us consider the right triangle ABC.Hypotenuse AB is radius itself.As long as R=1,AB=1.
(b)
sinα=hypotenuseopposite
sinα=ABBC BC is AB projection on y-axis,so that BC=y.
Then:
sinα=1ysinα=y (c)
cosα=hypotenuseadjacent
cosα=ABAC AC is AB projection on x-axis,so that AC=x.Then:
cosα=x
At the point where
α=23πx=0 According to this,
cos23π=0
y=−1 And that is why
sin23π=−1Answer:
sin23π=−1
cos23π=0
Comments
Firstly notice that you can plot a point on a circle using coordinate, (cosx, sinx). Here the point (cos3 pi/2,sin3 pi/2) is the point (0,-1) on the unit circle.