[FONT="]The figure below shows two unit circles. The first is centered at the origin and the second at [/FONT]
[FONT="]the point T = ( 2 , 0 ). [/FONT]
[FONT="]Note that: ( i ) segment RQ is tangent to the second circle, [/FONT]
[FONT="]( ii ) P is the point where segment RQ intersects the first circle, [/FONT]
[FONT="]( iii ) the point R has coordinates ( -1 , 0 ). [/FONT]
[FONT="]Carry-out the following steps to find the exact coordinates of the points P and Q [/FONT]
[FONT="]( a ) Observe that RQT is right. [/FONT]
[FONT="]Use the Pythagorean Theorem to find the length of side QR . [/FONT]
[FONT="]( b ) Find the tangent of angle theta [/FONT]
[FONT="]( c ) Write the equation of line RQ . (Hint: tan theta = slope of RQ .) [/FONT]
[FONT="]( d ) Find the coordinates of point P [/FONT]
[FONT="](Hint: Solve simultaneously the equations which describe line RQ and the first [/FONT]
[FONT="]unit circle.) [/FONT]
[FONT="]( e ) Find the coordinates of point Q [/FONT]
[FONT="](Hint: Compare cos theta and sin theta as described in the right triangles RQT and [/FONT]
[FONT="]RSQ)
[/FONT][FONT="]I am just having trouble with parts d and e.
[/FONT]
[FONT="]the point T = ( 2 , 0 ). [/FONT]
[FONT="]Note that: ( i ) segment RQ is tangent to the second circle, [/FONT]
[FONT="]( ii ) P is the point where segment RQ intersects the first circle, [/FONT]
[FONT="]( iii ) the point R has coordinates ( -1 , 0 ). [/FONT]
[FONT="]Carry-out the following steps to find the exact coordinates of the points P and Q [/FONT]
[FONT="]( a ) Observe that RQT is right. [/FONT]
[FONT="]Use the Pythagorean Theorem to find the length of side QR . [/FONT]
[FONT="]( b ) Find the tangent of angle theta [/FONT]
[FONT="]( c ) Write the equation of line RQ . (Hint: tan theta = slope of RQ .) [/FONT]
[FONT="]( d ) Find the coordinates of point P [/FONT]
[FONT="](Hint: Solve simultaneously the equations which describe line RQ and the first [/FONT]
[FONT="]unit circle.) [/FONT]
[FONT="]( e ) Find the coordinates of point Q [/FONT]
[FONT="](Hint: Compare cos theta and sin theta as described in the right triangles RQT and [/FONT]
[FONT="]RSQ)
[/FONT][FONT="]I am just having trouble with parts d and e.
[/FONT]