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]}