Montana Math MT.PLUS.ALG.TRIG.1.a
The Standard
- MT.PLUS.ALG.TRIG.1
- Understand how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers by: Defining the sine and cosine functions in terms of the unit circle, and Defining the tangent, cotangent, secant, and cosecant functions in terms of sine and cosine.
Understand how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers by: Defining the sine and cosine functions in terms of the unit circle, and
2026 Montana Mathematics Content Standards · Algebraic and Functional Reasoning
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students locate the endpoint of an angle on a circle of radius 1. They read its horizontal coordinate as cosine and its vertical coordinate as sine, including for negative angles and angles past one full turn.
What Mastery Looks Like
- They plot −π/2 and 3π/2 at (0, −1), then give cosine 0 and sine −1 for both. They explain why adding a full turn leaves both values unchanged.
Common Misconceptions
- Students may swap the coordinates, calling the horizontal coordinate sine. They may think negative angles are invalid or that angles past one full turn have new endpoints. Some expect sine and cosine to be positive because the radius is 1.
How to Assess It
- Exit ticket: Mark the endpoints for −π/2 and 3π/2 on a unit circle. Write sine and cosine for each angle, then explain why the values match.
Lesson moves
Ways to Teach It
Fasten a paper arrow to a unit circle marked in radians, rotate it to −π/3 and 5π/3, and record the endpoint coordinates.
Ask students to write why π/3 and 7π/3 have matching sine and cosine, using their endpoints as evidence.
Give teams angle cards and coordinate cards, including −π/2, 3π/2, and (0, −1), then have them make and justify matches.
Sketch a Ferris wheel centered at the origin with radius 1, then compare a seat’s height at π/2 and 5π/2.
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Related Standards
- MT.PLUS.ALG.TRIG.1
Understand how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers by: Defining the sine and cosine fun...
- MT.PLUS.ALG.TRIG.1.b
Defining the tangent, cotangent, secant, and cosecant functions in terms of sine and cosine.
- MT.PLUS.ALG.TRIG.3.a
Graphing sine and cosine functions, identifying period, midline, and amplitude, and
- MT.CORE.GEOM.MEAS.3.a
Deriving and applying the trigonometric ratios in special right triangles, and
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