Sine, Cosine, and Tangent
Everything trigonometric starts at one picture: an angle in standard position crossing the circle of radius 1. The crossing point is (cos θ, sin θ), so cosine is the x-coordinate, sine is the y-coordinate, and tangent is the slope of the terminal ray, sine over cosine. Radians measure the arc the angle cuts on that circle, with π radians equal to 180 degrees, and angles a full turn apart share a terminal ray and all three values.
The mistakes are picture mistakes: swapping which coordinate is which, dropping a sign by ignoring the quadrant, treating a bare number like 2 as degrees when it is radians, and leaving the calculator in degree mode. The lesson drills the picture until the swaps stop landing.
The work
3 ways in · any order
Lesson
Sine, Cosine, and Tangent
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Cosine first, sine second: the terminal point is (cos θ, sin θ), and tangent is the ray's slope. The lesson builds the unit-circle picture, the radian-degree bridge, and coterminal reasoning, then closes with ten scenarios on coordinates, conversions, slopes, and the calculator mode trap.
Diagnostic
10-item topic check
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Ten items spanning the two Topic 3.2 misconceptions: degree-radian unit slips and coordinate or sign errors at the unit circle. 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.