What are the coordinates for the point $p(45^circ)$ where $p(theta)=(x,y)$ is the point where the terminal arm of an angle $theta$ intersects the unit circl?

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Answer 1 · 2018-08-03T08:42:42

$( 1/sqrt2, 1/sqrt 2 )$ . See graphical depiction.

The polar equation of this unit circle is $r = 1$ .

A point of the radial line $vec(OP)$ , in the direction $theta$ are

$p ( theta ) = r ( cos theta, sin theta )$ .

If P is the point of intersection with r = 1,

$p ( theta ) = ( cos theta, sin theta )$ .. So,

$p ( pi/4 ) = ( cos (pi/4), sin (pi/4)) = ( 1/sqrt 2, 1/sqrt 2 )$ .

See graphical depiction.

graph{(x^2+y^2-1)(y-x)((x-1/sqrt2)^2+(y-1/sqrt2)^2-0.001)=0[0 2 0 1]}

What are the coordinates for the point p(45^circ)p(45^circ) where p(theta)=(x,y)p(theta)=(x,y) is the point where the terminal arm of an angle thetatheta intersects the unit circl?