2 Unit Circles on a Coordinate Plane

Jetstreak

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

( e ) Find the coordinates of point Q
(Hint: Compare cos theta and sin theta as described in the right triangles RQT and
RSQ)
I am just having trouble with parts d and e.
attachment.php
What is the equation of the the first unit circle?

What is the equation of the line RQ?
 
I know the equation of line RQ. It is: (x+1)/3
But I am not sure what you mean by the equation of the unit circle.
General equation of a circle:

(x-h)2 + (y-k)2 = r2

Where:

The co-ordinate of the center is (h,k) and the length of the radius = r
 
I know the equation of line RQ. It is: (x+1)/3 ← That is not an equation. "Equation" must have an "equal to" statement.
But I am not sure what you mean by the equation of the unit circle.
.
 
I know the equation of line RQ. It is: (x+1)/3 NO! It is not.
But I am not sure what you mean by the equation of the unit circle.

RQ:  y=18(x+1)\displaystyle \large{\overleftrightarrow {RQ}:\;y = \frac{1}{{\sqrt 8 }}\left( {x + 1} \right)}
 
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