Florida B.E.S.T. MA.912.T.2.3
The Standard
Determine the values of the six basic trigonometric functions for 0, π/6, π/3 and π/4 and their multiples using special triangles.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students use special-triangle side ratios to calculate exact trigonometric values. They connect angles to reference angles, determine quadrant signs, and use reciprocal relationships for secant, cosecant, and cotangent.
What Mastery Looks Like
- A student can explain values such as sin(π/3) = √3/2 using a special triangle. The student can find all six values for related angles, choose correct signs, and identify undefined results.
Common Misconceptions
- Students may swap sine and cosine or use side lengths instead of side ratios. They often ignore quadrant signs, rationalize incorrectly, or miss when tangent, cotangent, secant, or cosecant is undefined.
How to Assess It
- Exit ticket: Find all six trigonometric values for 7π/6. Show the reference triangle, quadrant signs, and exact simplified values.
Lesson moves
Ways to Teach It
Cut paper 30-60-90 and 45-45-90 triangles, label side ratios, then place copies in each quadrant of a unit circle.
Ask students to write why cos(5π/4) is negative while its reference value has magnitude √2/2.
Give pairs a card sort matching angles, reference angles, quadrants, and exact values for the six functions.
Model a Ferris wheel with a paper plate and calculate exact horizontal and vertical positions at special angles.
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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
Define and use trigonometric ratios, identities or functions to solve problems.
- MA.912.T.2.2
Define the six basic trigonometric functions for all real numbers by identifying corresponding angle measures and using right triangles drawn in the unit circle...
- MA.912.T.2
Extend trigonometric functions to the unit circle.
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