Radians and the unit circle

Problem types

• Angular and linear velocity
• Reference angles and standard position
• Enter a degree-radian conversion
• Radians from an arc
• Degrees and radians
• Coordinates on a unit circle
• Why the unit circle defines sine and cosine for every real number
• Complete the explanation from a real number to sine and cosine
• Where a real number lands on the unit circle
• Real numbers that share a terminal point

Builds on

• Arc length and sector area
• Side ratios of special right triangles
• Why every circle is similar to every other · Earlier idea

  All circles are similar, so arc length divided by radius is the same for a given central angle, and that ratio is the angle in radians.

• Theorems about circles · Earlier idea

  Central angles and arcs correspond, and radians measure a central angle as arc length divided by radius.

• Telling time to five minutes · Earlier idea

  A clock hand sweeps a full turn in 60 minutes, which is the idea behind angular velocity and measuring a turn in radians.

Leads to

• Period, amplitude, and midline
• The complex plane
• Polar and Cartesian coordinates
• Exact values at special angles
• Pythagorean and angle-sum identities
• Odd, even, and periodic trig functions

Related skills

None listed.