Unit Circle and Radian Measure

ACT Math · Axiom Academy

LESSON Unit Circle and Radian Measure Degrees, radians, and the coordinates that define every trig value. A radian is the angle created when the arc length equals the radius of the circle. It is the "natural" unit for measuring angles in mathematics. One full revolution, in each language 2. Converting Between Degrees and Radians Because , converting is just multiplying by a fraction that cancels the unit you're leaving. Watch both dials below sweep in lockstep — the degree reading and the radian reading are the same angle, named two ways. Degrees → radians: multiply by Radians → degrees: multiply by ACT Practice: radian conversion What is the radian measure of 225° ? (A) (B) (C) (D) (E) You need these conversions cold for the ACT. Watch each standard angle fan out around the circle with its radian name — the whole board is just a repeat of the denominators 6, 4, 3, 2 . The unit circle is a circle of radius 1 centered at the origin. For any angle , the point on the circle is exactly . Watch the coordinate readout update as the point rides around and pauses at each first-quadrant landmark. Start on the positive x -axis. Low, wide — mostly across, a little up. The balanced point — x equals y . High, narrow — the mirror of 30° . 5. Reading Trig Values from the Unit Circle Since each point is , the coordinates are the trig values. Watch the point drop a vertical shadow onto the x -axis (that length is ) and a horizontal shadow onto the y -axis (that length is ).

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