Montana Math MT.PLUS.ALG.TRIG.3.a
The Standard
- MT.PLUS.ALG.TRIG.3
- Graph trigonometric functions with and without the use of technology by: Graphing sine and cosine functions, identifying period, midline, and amplitude, and Graphing tangent functions, identifying period and asymptotes.
Graph trigonometric functions with and without the use of technology by: Graphing sine and cosine functions, identifying period, midline, and amplitude, and
2026 Montana Mathematics Content Standards · Algebraic and Functional Reasoning
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students sketch sine and cosine curves using key points, then check their sketches with a graphing tool. They find the midline, amplitude, and period from an equation or graph.
What Mastery Looks Like
- Given y = 2cos(x) + 1, a student plots one full cycle by hand. They label the midline y = 1, amplitude 2, and period 2π, then check their sketch with a graphing tool.
Common Misconceptions
- Students may call the full distance from trough to peak the amplitude instead of halving it. They may use the x-axis as the midline after a vertical shift or mistake half a cycle for the full period.
How to Assess It
- Exit ticket: Sketch one cycle of y = 2sin(x) + 1 from 0 to 2π without a calculator. Label five key points, the midline, amplitude, and period.
Lesson moves
Ways to Teach It
Use a paper unit circle and graph paper; mark five quarter-turn angles, then plot each point's horizontal and vertical coordinates against angle.
In Desmos, compare sin(x) and sin(x) + 2; write two sentences explaining what moved and which measurements stayed the same.
Match equation cards for sin(x), cos(x), 2sin(x), and sin(2x) to printed graphs; label each graph's midline, amplitude, and period.
Plot Ferris wheel heights of 2, 12, 22, 12, 2 meters at 0, 5, 10, 15, 20 minutes; find the midline and cycle length.
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Related Standards
- MT.PLUS.ALG.TRIG.3.b
Graphing tangent functions, identifying period and asymptotes.
- MT.PLUS.ALG.TRIG.1.a
Defining the sine and cosine functions in terms of the unit circle, and
- MT.PLUS.ALG.TRIG.3
Graph trigonometric functions with and without the use of technology by: Graphing sine and cosine functions, identifying period, midline, and amplitude, and Gra...
- MT.PLUS.ALG.TRIG.1.b
Defining the tangent, cotangent, secant, and cosecant functions in terms of sine and cosine.
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