Montana Math MT.PLUS.ALG.TRIG.3.b
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 tangent functions, identifying period and asymptotes.
2026 Montana Mathematics Content Standards · Algebraic and Functional Reasoning
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students sketch tangent graphs by hand and check them with a graphing tool. They find the period, mark vertical asymptotes, and draw the branches between them.
What Mastery Looks Like
- Given y = tan(2x), a student marks the nearest asymptotes at −π/4 and π/4 and gives the period as π/2. Their sketch passes through the origin and approaches, but never touches, the asymptotes.
Common Misconceptions
- Students may give tangent a period of 2π because sine and cosine have that period. Some plot a point where tangent is undefined or draw the curve crossing an asymptote.
How to Assess It
- Exit ticket: Sketch one branch of y = tan(2x). Label its period and the two asymptotes nearest the origin.
Lesson moves
Ways to Teach It
Give pairs unit-circle cards and graph paper; calculate sin x divided by cos x, plot the results, and mark angles where division is undefined.
Show graphs of tan x and tan(2x); ask students to explain why the asymptotes are closer together on the second graph.
Play a matching game with cards showing tangent equations, periods, asymptotes, and graphs, including tan x and tan(2x).
Sketch a ramp with a 2-meter horizontal run; calculate its rise at 5°, 10°, and 15° using 2tan(angle), then plot.
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Related Standards
- 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...
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- MT.PLUS.ALG.EXP.4
Graph logarithmic and exponential functions with and without the use of technology by identifying intercepts, asymptotes, and end behavior.
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