Montana Math MT.PLUS.ALG.TRIG.3

MT.PLUS.ALG.TRIG.3 is a cluster heading. These are the individual standards under it.

• MT.PLUS.ALG.TRIG.3.a

  Graphing sine and cosine functions, identifying period, midline, and amplitude, and

• MT.PLUS.ALG.TRIG.3.b

  Graphing tangent functions, identifying period and asymptotes.

01

What Students Need to Do

Students sketch sine and cosine waves and label their midlines, amplitudes, and periods. They graph tangent in separate branches, marking its period and vertical asymptotes. They work by hand and check their graphs with a graphing tool.

02

What Mastery Looks Like

Given y = 3cos(2x) - 1, a student marks a midline of -1, amplitude of 3, and period of π, then sketches a cycle. For y = tan(2x), they place asymptotes at x = ±π/4 and repeat the branches every π/2.

03

Common Misconceptions

Students may assume the midline is always the x-axis or mistake the full peak-to-trough distance for amplitude. They may draw tangent through its asymptotes or give it a period of 2π instead of π.

04

How to Assess It

Ask students to sketch y = 2sin(x) + 1 and y = tan(x) from 0 to 2π. Have them label the sine graph's amplitude, midline, and period, and the tangent graph's period and asymptotes.

1. 01

   Use a paper unit circle and ruler to plot each point's x- and y-coordinates against angle, building cosine and sine graphs.

2. 02

   Show y = 2sin(x) + 1 beside y = sin(x), and ask students which has the higher midline and larger amplitude.

3. 03

   Give pairs graph cards and feature cards to match sine and cosine amplitudes and midlines, and tangent periods and asymptotes.

4. 04

   Sketch a seat's height over two 60-second turns on a Ferris wheel of radius 20 feet, starting 2 feet above ground.

• MT.PLUS.ALG.EXP.4

  Graph logarithmic and exponential functions with and without the use of technology by identifying intercepts, asymptotes, and end behavior.

• MT.PLUS.ALG.TRIG.4

  Solve trigonometric equations with and without the use of technology.