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 180
^{o}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 30
^{o}or 45^{o} - identify and justify relationships between coordinate points on the unit circle
*Example: describe how the coordinates of 30*^{o}and 60^{o}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)

- justify coordinates on the unit circle as (cosθ, sinθ)

- graph the
**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 30^{o}or 45^{o}- use reference angles to evaluate a trig expression
- justify why the tangent of 90
^{o}and 270^{o}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: sin163*^{o}is between ½ and 0 because sin163^{o}falls between sin150^{o}and sin180^{o}, or sin163^{o}is between ½ and 0 because the terminal side is in Q2 where y is positive and the right triangle‘s base angle is 17^{o}and sin17^{o }must be less than sin30^{o}= 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