Lesson 4.1
Radians and Arc Length
A radian measures an angle by the ratio of arc length to radius. Use radians in arc-length and sector-area formulas. Convert degrees before substituting, and distinguish arc length from the straight chord length.
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Unit 4
Unit Circle and Trigonometric Functions
Extending trigonometry beyond right triangles. Structure and symmetry replace memorisation, which is what makes unfamiliar angles tractable.
Lessons and exercises
Lesson 4.2
Unit Circle Coordinates
A point on the unit circle at angle theta has coordinates cosine theta and sine theta. Reference angles give magnitudes, while the quadrant sets signs. Angles that differ by full revolutions reach the same point.
Lesson 4.3
The Six Functions
Sine and cosine are unit-circle coordinates; tangent is their quotient. Cosecant, secant, and cotangent are reciprocals. A zero denominator makes a ratio undefined, so check the angle before taking a reciprocal.
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