QuestionIdentify the false statement about the unit circle: A. ; B. radius 1 at origin; C. infinite integer points; D. if .
Studdy Solution
STEP 1
Assumptions1. We understand the definition of a unit circle a circle with a radius of1, centered at the origin of a coordinate plane.
. We understand that integer coordinates are points where both the x and y values are integers.
3. We understand the equation of a circle in a coordinate plane , where (h, k) is the center of the circle and r is the radius.
STEP 2
Let's analyze each statement one by one.Statement A The equation of the unit circle is .
This is the equation of a circle centered at the origin (0,0) with radius1. So, statement A is true.
STEP 3
Statement B The unit circle is a circle centered at the origin with radius1.
This is the definition of a unit circle. So, statement B is true.
STEP 4
Statement C There are infinitely many points that lie on the graph of the unit circle that have integer coordinates.
Let's analyze this statement. A point with integer coordinates on the unit circle would satisfy the equation , where x and y are integers. The only integer solutions to this equation are (1,0), (0,1), (-1,0), and (0,-1). So, there are not infinitely many points with integer coordinates on the unit circle. Therefore, statement C is not true.
STEP 5
Statement D A point lies on the graph of the unit circle if and only if .
This is the definition of a point on the unit circle. So, statement D is true.
The statement that is not true is C There are infinitely many points that lie on the graph of the unit circle that have integer coordinates.
Was this helpful?
