Trigonometry
Undergraduate · Math
Syllabus focus
Topics typically covered
Click a topic for the full text and related unit practice.
Undergraduate Trigonometry — scope drawn from OpenStax Algebra and Trigonometry 2e (trig chapters) and OpenStax Precalculus 2e trig units.
Circular functions
- Angles in degrees and radians — Angles in degrees and radians; arc length and sector area
- The unit circle and reference angles — The unit circle and reference angles
- Sine, cosine, and tangent: definitions and graphs — Sine, cosine, and tangent: definitions and graphs
- Cosecant and secant — Cosecant and secant
- Cotangent (where covered) — Cotangent (where covered)
- Amplitude, period, and phase shift — Amplitude, period, and phase shift
- Vertical shift — Vertical shift
Identities and equations
- Pythagorean and reciprocal identities — Pythagorean and reciprocal identities
- Quotient identities — Quotient identities
- Sum, difference, and double-angle identities — Sum, difference, and double-angle identities
- Half-angle formulas — Half-angle formulas
- Product-to-sum — Product-to-sum
- Sum-to-product identities (optional) — Sum-to-product identities (optional)
- Solving basic trigonometric equations — Solving basic trigonometric equations
- Inverse trigonometric functions: domains and ranges — Inverse trigonometric functions: domains and ranges
Triangles and polar form
- Right triangle trigonometry — Right triangle trigonometry
- Applications — Applications
- Law of sines and law of cosines — Law of sines and law of cosines
- Area of a triangle using trigonometry — Area of a triangle using trigonometry
- Polar coordinates — Polar coordinates
- Conversion to/from rectangular form — Conversion to/from rectangular form
- De Moivre's theorem — De Moivre's theorem
- Roots of complex numbers (introduction) — Roots of complex numbers (introduction)
Study units
Each unit includes a study guide, worksheets, review, practice test, and answer key. One unit is free; subscribe for the full class.
- Circular functions
Angles in degrees and radians; arc length and sector area
Coming soon - Identities and equations
Pythagorean and reciprocal identities
Coming soon - Triangles and polar form
Right triangle trigonometry
Coming soon
Notes
Undergraduate Trigonometry — scope drawn from OpenStax Algebra and Trigonometry 2e (trig chapters) and OpenStax Precalculus 2e trig units. Topic outline: `content/topics/undergraduate/trigonometry.json`.