Sine and Cosine Function Graphs
Ride the unit circle and record coordinates: the height trace is the sine curve, starting at 0 and rising; the x-coordinate trace is the cosine curve, starting at its peak of 1. Both share period 2π, amplitude 1, midline y = 0, and range [−1, 1]; they differ only in phase, with cosine equal to sine slid left by a quarter period. Each curve is concave down above the midline and concave up below it, so the bend switches at the midline crossings.
The mistakes are location and measurement mistakes: starting sine at the peak or cosine at zero, quoting the full 2-unit swing as amplitude, placing zeros and extremes at the wrong quarter marks, and sliding sine the wrong way to reach cosine. The lesson pins every feature to its spot on the circle.
The work
3 ways in · any order
Lesson
Sine and Cosine Function Graphs
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Sine starts at zero rising; cosine starts at one falling: the same wave a quarter turn apart. The lesson unwraps the circle into both parent curves, locates every zero, peak, and inflection, then closes with ten scenarios reading and comparing the two graphs.
Diagnostic
10-item topic check
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Ten items spanning the two Topic 3.4 misconceptions: amplitude and midline misreads on the parent curves, and circle-to-graph location errors for zeros, peaks, and starting values. Results route you to the drills that fix what fired.
Targeted Practice
Drill a single misconception
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Pick one of the failure modes you missed and drill it on its own. The round is adaptive: two correct in a row clears the misconception and moves you to the next.