Standard syllabus
Trigonometry · Undergraduate · Math
Learning objectives from the Trigonometry syllabus, grouped by unit. Click an objective for study materials.
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)
Learning objectives
Click an objective for study materials.
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)
Multi-Unit Problems
Course-level sets that combine skills across study units (coming soon).
Browse Multi-Unit ProblemsWhat each unit includes
Open a unit below for full materials. Typical resources:
- Study guide
- Exam Strategy
- Common Mistakes
- Worksheets
- Word problems
- Mixed Practice
- Multi-Unit Problems
- Review
- Practice test
- Answer key
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
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