10 Components
Big Ideas
Formative Assessment Lesson
End of Unit Assessments
Browse Components
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

No Core Resource for this Big Idea.

Consider using the Instructional Routines linked below for teaching towards this Big Idea.