Public learning track
Unit Circle Analysis and Arbitrary Angles
10th Grade · Math · Open Global Math
8 lessons
Goal
Extend trigonometric functions to all real numbers using standard position, reference angles, quadrant signs, and Pythagorean identities on the unit circle.
Featured Diagrams
Angles in Standard Position and Coterminal Angles
8 lessons
0 of 8 done
- 1Angles in Standard Position and Coterminal AnglesUp nextStart
- 2Reference Angles Across All Four QuadrantsPremiumNot started yet
- 3Defining Trigonometric Functions Using the Unit CircleNot started yet
- 4Quadrant Signs and Tangent on the Unit CircleNot started yet
- 5Exact Trigonometric Values on the Unit CircleNot started yet
- 6Reciprocal Trigonometric Functions: Secant, Cosecant, CotangentNot started yet
- 7Using the Pythagorean Identity to Find tan(θ) Given sin(θ) or cos(θ)Not started yet
- 8Evaluating Trigonometric Functions for Negative and Large AnglesNot started yet
Curriculum Framework
10th Grade · Math · Open Global Math
1
10 lessons
Right Triangle Trigonometry and Exact Values
Apply trigonometric ratios, complementary angle relationships, exact special right triangle values, and 2D/3D geometric reasoning to solve right triangles in applied contexts.
2
10 lessons
Non-Right Triangles: Law of Sines, Law of Cosines, and Area
Derive and apply the Law of Sines, Law of Cosines, and the sine area formula to solve oblique triangles in navigation, surveying, and vector modeling.
3
6 lessons
Radian Measure, Arc Length, and Sector Area
Define radians through arc length proportionality, derive sector and segment area formulas, and solve rotational and circular motion problems.
4
8 lessons
Unit Circle Analysis and Arbitrary Angles
Extend trigonometric functions to all real numbers using standard position, reference angles, quadrant signs, and Pythagorean identities on the unit circle.
5
8 lessons
Modeling Periodic Phenomena with Trigonometric Functions
Graph transformed sine and cosine functions and build sinusoidal models for real-world cyclical behavior including tides, temperatures, and harmonic motion.