10 Components
Big Ideas
Formative Assessment Lesson
End of Unit Assessments
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Big Ideas
Formative Assessment Lesson
End of Unit Assessments
Big Idea:

The Unit Circle illustrates properties of trigonometric functions.

1 week

Evidence of Understanding

• explain patterns in the unit circle
• graph the unit circle and identify its center, radius, intercepts, domain, and range
• use the unit circle’s radius to explain why 180o is equivalent to π
• create diagrams that illustrate equivalent degree and radian measures
• describe how degrees and radians are related
• convert between degrees and radians
• approximate the degree measure for a single radian
• use transformations and special triangles to find points on the unit circle for central angles that are multiples of 30o or 45o
• identify and justify relationships between coordinate points on the unit circle
• Example: describe how the coordinates of 30o and  60o are related, etc.
• describe the relationship between the angle measure and the sign value of its coordinates
• Example: any angle with a terminal side in the second quadrant has coordinates (-x, + y)
• prove the Pythagorean Identity sin2θ + cos2θ = 1
• justify coordinates on the unit circle as (cosθ, sinθ)

• use the unit circle to extend understanding of trigonometry
• justify intervals when values of sinθ or cosθ increase or decrease from a diagram or table
• explain why the sine or cosine of any angle must be between 1 and -1, inclusively
• determine the exact value of any sine, cosine, tangent, cosecant, secant, or cotangent expression for angles that are multiples of 30o or 45o
• use reference angles to evaluate a trig expression
• justify why the tangent of 90o and 270o are undefined
• explain why the tangent values are positive in quadrants 1 and 3
• approximate the value of any sin, cos, tan, csc, sec, or cot expression from the unit circle
• Example: sin163o is between ½ and 0 because sin163o falls between sin150o and sin180o, or sin163o is between ½ and 0 because the terminal side is in Q2 where y is positive and the right triangle‘s base angle is 17o and sin17o must be less than sin30o = ½
• use properties of the unit circle to solve for an unknown angle in a trig equation

Develop conceptual understanding:

unit circle, radian, Pythagorean Identity, tangent, cosecant, secant, cotangent, undefined

Supporting terms to communicate:

circle, center, radius, intercepts, domain, range, degree, special triangles, reflection, rotation, terminal side, quadrant, sine, cosine
Core Resource
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