Trigonometry
Undergraduate · Math
Syllabus focus
Standard syllabus · STEM / applied
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$1,162 · Trigonometry · 18 tutoring hrs
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Topics typically covered
Standard syllabus
Circular functions
- Angles in degrees and radians; arc length and sector area
- The unit circle and reference angles
- Sine, cosine, and tangent: definitions and graphs
- Cosecant, secant, and cotangent (where covered)
- Amplitude, period, phase shift, and vertical shift
Identities and equations
- Pythagorean, reciprocal, and quotient identities
- Sum, difference, double-angle, and half-angle formulas
- Product-to-sum and sum-to-product identities (optional)
- Solving basic trigonometric equations
- Inverse trigonometric functions: domains and ranges
Triangles and polar form
- Right triangle trigonometry and applications
- Law of sines and law of cosines
- Area of a triangle using trigonometry
- Polar coordinates and conversion to/from rectangular form
- De Moivre's theorem and roots of complex numbers (introduction)
STEM / applied
Vectors and engineering applications
- Vectors in the plane; dot product and angle between vectors
- Resultant forces and component decomposition
- Simple harmonic motion and sinusoidal modeling
- AC circuits: phase and impedance (introductory overview)
- Navigation, surveying, and bearing problems
Technology and modeling
- Graphing trigonometric functions with technology
- Regression and curve fitting for periodic data
- Damped oscillations and envelope curves (preview)
- Spherical coordinates and 3D applications (optional)
Notes
Topics reflect common college trigonometry syllabi at US institutions. Many students encounter this material within a precalculus or calculus preparation sequence rather than as a standalone course.