NY Next Generation Math AII-F.TF.2
The Standard
Apply concepts of the unit circle in the coordinate plane to calculate the values of the six trigonometric functions given angles in radian measure.
New York State Next Generation Mathematics Learning Standards
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students use a point on the unit circle to calculate sine, cosine, tangent, and their reciprocal functions for a radian angle. They attend to signs and undefined ratios by quadrant.
What Mastery Looks Like
- Given a unit-circle point, the student finds all six trigonometric values and identifies any undefined value. The student explains each ratio from the coordinates.
Common Misconceptions
- Students may swap sine and cosine, ignore quadrant signs, or take a reciprocal of zero. They may use degree-mode calculator values for radian inputs.
How to Assess It
- Give a unit-circle point in quadrant II and its radian angle. Ask for all six trigonometric values with one sentence explaining an undefined case.
Lesson moves
Ways to Teach It
Place coordinate cards on a large unit circle, then derive all six ratios at selected angles.
Ask how a quadrant determines which trigonometric values are negative.
Play six-function relay with radian cards, coordinate pairs, ratios, and undefined-value checks.
Use a rotating arm model to calculate horizontal, vertical, and reciprocal ratios at a given angle.
Keep exploring
Related Standards
- AII-F.TF.4
Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.
- AII-F.TF.1
Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.
- GEO-G.C.2.b
Identify, describe and apply relationships among radii, chords, tangents, and secants of a circle.
- GEO-G.C.2.a
Identify, describe and apply relationships between the angles and their intercepted arcs of a circle.
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