Florida B.E.S.T. MA.912.T.2.2
The Standard
Define the six basic trigonometric functions for all real numbers by identifying corresponding angle measures and using right triangles drawn in the unit circle.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students map any real angle to a point, (x, y), on the unit circle. They use the coordinates and a reference triangle to define all six trigonometric functions. They also identify when a ratio is undefined.
What Mastery Looks Like
- Given an angle in degrees or radians, students locate its terminal side and find exact trigonometric values for common angles. They handle negative and coterminal angles, quadrant signs, reciprocals, and undefined values correctly.
Common Misconceptions
- Students often switch x and y for cosine and sine, or confuse reciprocal functions with inverse functions. They may ignore quadrant signs or use right-triangle ratios only for acute angles. Some assign values when a denominator is zero.
How to Assess It
- Exit ticket: Draw the terminal side for 5π/6, label its unit-circle point, and find exact values of all six trigonometric functions.
Lesson moves
Ways to Teach It
Give pairs a paper unit circle and reference triangles to place, then have them label x, y, and all six function ratios.
Ask students to explain why tangent is undefined at π/2 while sine still has a value.
Play a matching game with angle cards, coordinate cards, and six-function value cards for common unit-circle angles.
Model a Ferris wheel point on a unit circle, then connect its horizontal and vertical positions to cosine and sine.
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Printable MA.912.T.2.2 Worksheet
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Related Standards
- MA.912.T.2.5
Given angles measured in radians or degrees, calculate the values of the six basic trigonometric functions using the unit circle, trigonometric identities or te...
- MA.912.T.1.1
Define trigonometric ratios for acute angles in right triangles.
- MA.912.T.2.3
Determine the values of the six basic trigonometric functions for 0, π/6, π/3 and π/4 and their multiples using special triangles.
- MA.912.T.2
Extend trigonometric functions to the unit circle.
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