Gain understanding in radian measure of an angle, represented by the length of the arc on a unit circle. Use the unit circle to extend trigonometric functions to all real numbers interpreted using radian measures of angles. Utilize special triangles to geometrically determine values for sine, cosine, and tangent and express their values using the unit circle.

Use the unit circle to demonstrate symmetry and periodicity of trigonometric functions. Apply trigonometric functions to model periodic phenomena with specific amplitude, frequency, and midline. Comprehend that limiting a trigonometric function to an area where it is consistently increasing or decreasing enables the creation of its inverse. Solve trigonometric equations that appear in modeling contexts using inverse functions; assess the solutions via technology and interpret them contextually.

Demonstrate the Pythagorean identity and use it to find sin(θ), cos(θ), or tan(θ) given the angle's quadrant. Validate the addition and subtraction formulas for sine, cosine, and tangent and employ them to solve problems.