Evidence of Understanding

**describe the properties of a circle**- explore the relationship between a center point and a fixed distance (radius) rotated around it
- define a circle using the center, radius, and lines of symmetry

- use tools to inductively show the
**circumference**of a circle is 2πr - explain the relationship between the central angle of a circle and its
**arc measure**- describe a circle using 360
^{o }degrees and 2π**radians**or 180^{o}and π radians

- describe a circle using 360

- explore the relationship between a center point and a fixed distance (radius) rotated around it
**graph the equation of a circle in the coordinate plane**- given any equation
*(x - h)*^{2}^{}+ (y - k)^{2}*= r*^{2}*,*describe how x, y, h, k, and r impact the graph - find the center and the radius of a circle by completing the square
- given a coordinate point, use the graph or equation toprove if it lies on the circle
- given a coordinate point, use symmetry to justify other points on the circle
- use Pythagorean Theorem to identify the radius, center, or points that lie on the circle
- explain the connection of the equation of a circle and Pythagorean Theorem

- explain the connection of the equation of a circle and Pythagorean Theorem

- given any equation
**use triangles and trigonometry to describe the graph of a circle**- given the center, radius and the
**terminal side**of any angle between 0^{o }and 360^{o }, find the coordinates of the corresponding point on the circle- use the properties of
**special right triangles**(30-60-90 and 45-45-90) - describe the relationship between
**cosine**and the x coordinate of a point on the circle - describe the relationship between
**sine**and the y coordinate of a point on the circle

- use the properties of
- prove sin
^{2 }θ + cos^{2 }θ = 1 - use transformations to describe and justify the relationship between coordinate points that share a
**reference angle**- Ex: the points at 30
^{o }and 150^{o }are similar because the right triangle is reflected - Ex: the points 30
^{o }and 120^{o }are similar because the right triangle is rotated

- Ex: the points at 30
- given the center and any point on the circle, use inverse trig functions (sin
^{-1}, cos^{-1}, and tan^{-1}) to find the measure of the circle’s corresponding central angle

- given the center, radius and the

Develop conceptual understanding:

circle, circumference, arc measure, radian, terminal side, special right triangle (30-60-90 and 45-45-90), cosine, sine, reference angleSupporting terms to communicate:

center, radius, central angle, degrees, symmetrical, reflect, completing the square, quadrant, Pythagorean Theorem, right triangle, reflection, rotation, inverse trig