Convert fluently between degrees and radians, find coterminal and reference angles, and compute arc length and angular or linear velocity.
A radian measures an angle by comparing arc length to radius: one radian is the angle where the arc length exactly equals the radius. A full circle measures 2*pi radians (about 6.28), matching its own circumference-to-radius ratio, instead of the arbitrary 360 that degrees use. Convert degrees to radians by multiplying by pi/180; convert radians to degrees by multiplying by 180/pi.
Two angles are COTERMINAL if they share the same initial and terminal side -- you reach one from the other by adding or subtracting full rotations (360 degrees, or 2*pi radians). The REFERENCE angle is the acute angle between the terminal side and the x-axis; it is always positive and between 0 and 90 degrees, and it is the key to finding exact trig values in any quadrant, starting next week.
Arc length uses s = r*theta, with theta measured in RADIANS (this formula only works in radians, part of why radians are the natural unit for a circle). Angular velocity (how fast an angle sweeps, in radians per unit time) multiplied by the radius gives linear velocity (how fast a point on the circle actually travels).
Mastery looks like: They convert fluently between degrees and radians, find coterminal and reference angles correctly in any quadrant, and compute arc length, angular velocity, and linear velocity.
Common stumbles: Using the wrong conversion factor (multiplying by 180/pi when radians were needed, or the reverse); plugging a degree measure directly into s=r*theta without converting to radians first.
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