Montana Math MT.PLUS.ALG.TRIG.4

MathGrades 9–12Trigonometric Functions

The Standard

Solve trigonometric equations with and without the use of technology.

2026 Montana Mathematics Content Standards · Algebraic and Functional Reasoning

Teacher's field guide

What Students Need to Do: Students solve trigonometric equations using algebra, unit-circle values, and inverse functions. They find every answer in a given interval or write solutions that repeat, then check their work with a graph or calculator.
What Mastery Looks Like: For sin x = 1/2 on 0 ≤ x < 2π, a student finds π/6 and 5π/6 and explains why both work. For all real x, they add 2πk to each answer, where k is any integer.
Common Misconceptions: Students often stop at the single answer shown by the inverse sine key. They may mix degrees and radians or add π instead of 2π when listing repeating sine solutions.
How to Assess It: Exit ticket: Solve sin x = 1/2 for 0 ≤ x < 2π and for all real x. Show how you found both angles, then check them with a calculator.

Lesson moves

Give students paper unit circles and two colored pencils to mark every angle where sin x = 1/2 between 0 and 2π.
Ask students to write: Why does a calculator show only π/6 for arcsin(1/2) when sin x = 1/2 has another answer?
Play whiteboard relay: solve cos x = −1/2 on [0, 2π), then check both answers on a graphing calculator.
Model a Ferris wheel seat’s height above center with 10 sin(πt/6); find when it reaches 5 meters during one 12-minute turn.

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