Unit 6:
Making Sense of Circles
G.GSR.7: Explore the concept of a radian measure and special right triangles.
G.GSR.8: Examine and apply theorems involving circles; describe and derive arc length and area of a sector; and model and explain real-life situations involving circles.
G.GSR.8: Examine and apply theorems involving circles; describe and derive arc length and area of a sector; and model and explain real-life situations involving circles.
Learning Goal:
- I can identify and use the properties of the circles to solve problems involving finding arcs, angles, and segments.
- I can read and write geometric notation for a segment or angle measure.
- I can solve problems involving major arcs, minor arcs, central angles, and measuring an arc as the measure of its corresponding central angle
|
|
|
|
Learning Goal:
- I can use similarity to derive that arc length and sector arc are proportional to the central angle that subtends it.
- I can solve situations involving finding the arc length or area sector [central angle]
when given the central angle [arc length or area sector]. θ must be in term of π
|
|
|
|
Learning Goal:
- I can describe the relationship and solve problems between inscribed angles.
- I can describe and solve problems involving a tangent line to a circle perpendicular to the radius at the point of tangency.
- I can describe relationships between central and circumscribed angles and use those relationships to solve problems.
- I can use angle measures formed by intersecting lines and circles to solve problems.
|
|
|
|
|
|
|
|
Learning Goal:
- I can derive the equation of a circle using the Pythagorean Theorem or Distance Formula
- I can graph and write an equation of a circle in standard form.
- I can graph an equation of the circle in general form using the complete the square to identify the center and radius.
|
|
|
|
Learning Goal:
- I can derive the unit circle using special right angles.
- I can represent special right triangles to identify common angles in quadrant one of the unit circles.
- I can use reflecting triangles to find the reference angles in the remaining quadrants.
- I can represent angles(degrees) in the coordinate plane as radian measures on the unit circle.
- I can convert between degree and radian measures.
- I can evaluate a trig function to find the coordinate value when given a common angle.
- I can evaluate an inverse trig function to find the degree.
|
|
|
|