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Trigonometry practice

Sine and Cosine Graphs worksheets

Graph transformed sine and cosine functions or write one valid equation from a graph, using exact radians or degrees.

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Draw each transformed graph or write one valid equation for the graph shown. Mark the midline and exact quarter-period key points.

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Build every curve from exact key points

The graph window spans two complete periods. Quarter-period ticks, the midline, and bounded amplitudes keep each transformation readable on paper.

Learning objective

What this activity builds

Connect amplitude, period, horizontal shift, vertical shift, and midline to exact quarter-period graph points.

Worked example

Graph y = −2 sin(2(x − π/4)) + 1.

Amplitude 2, period π, shift π/4 right, midline y=1.

Start at the shifted sine midline, then move by quarter-period steps of π/4. The negative amplitude sends the first quarter-step down to −1.

Teaching notes

Make the practice count

  • Find the period before choosing quarter-period x-values.
  • Draw the midline before plotting maxima and minima.
  • Accept algebraically equivalent equations when students read a graph.

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Choose radians or degrees and a bounded mix of graphing and equation-writing tasks. The same settings and seed reproduce every exact key point.

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Math SheetNameScoreTeacherDateSine and Cosine GraphsDraw each transformed graph or write one valid equation for the graph shown. Mark the midline and exact quarter-period key points.1. Draw the graph: y = -sin((x - pi/2)) + 2pi/2pi3pi/22pi5pi/23pi7pi/24pi9pi/2123midline y = 2xy2. Write one valid sine or cosine equation for the graph shown.-pi/40pi/4pi/23pi/4pi5pi/43pi/27pi/4-3-2-101midline y = -1xyEquation:Angles are in radians. Equivalent equations may use different phases or the other trig function.math-sheet.comPage 1 of 2
Math SheetNameScoreTeacherDateSine and Cosine GraphsDraw each transformed graph or write one valid equation for the graph shown. Mark the midline and exact quarter-period key points.3. Draw the graph: y = -3sin(1/2(x - 2pi))2pi3pi4pi5pi6pi7pi8pi9pi10pi-3-2-10123midline y = 0xy4. Write one valid sine or cosine equation for the graph shown.0pi/2pi3pi/22pi5pi/23pi7pi/24pi-101midline y = 0xyEquation:Angles are in radians. Equivalent equations may use different phases or the other trig function.math-sheet.comPage 2 of 2

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